GISAXS - User contributions [en]

GISAXS sample requirements

2014-09-23T00:42:42Z

130.199.3.165: /* Summary */

The following gives some rough guidelines for the kinds of samples suitable for [[GISAXS]]/[[GIWAXS]] measurements. In general, GISAXS is intended to measure thin films cast on flat substrates.

===Film Thickness===
Thin films From monolayers to microns can in principle be studied. Ideal film thickness is ~50 nm to ~300 nm; but ultimately it is the scientifically relevant thickness that should be targeted. Ultrathin layers will of course have lower total scattering intensity (and thus may require longer exposure times). Very thick (e.g. micron) layers can be studied with GISAXS, although the large roughness typical of such films will make some kinds of measurements impossible. In particular, the film will lack a well-defined [[critical angle]], which makes the usual above/below critical measurements impossible (and of course [[x-ray waveguiding]] will also not be possible).

===Substrate===
In principle any substrate can be used. However, GISAXS works best when the substrate is very smooth (on a nanometer and micron lengthscale), and also very flat (on a micron and macroscopic scale).
====Roughness====
If the substrate is rough, substantial [[diffuse scattering]] will be observed (possibly overwhelming the desired signal); and the film itself is likely to be rougher (making critical angle measurements difficult; see above).
====Flatness====
If the substrate is not flat:
# Sample alignment will be difficult, as there are in fact multiple sample planes.
# Relatedly, the incident angle may be ill-defined; measurements related to the critical angle will be similarly skewed (as there are multiple planes satisfying the critical angle).
# The measurements may be impacted, blurring/distorting the image.
# The specular x-ray beam itself may be focused or defocused (depending on the sign of the substrate curvature). In [[reflectivity]] measurements, this strongly skews the data (e.g. it can give rise to apparently greater than 100% reflection). In GISAXS, this effect may similarly distort intensities and peak widths.
Note that nominally flat substrates (e.g. silicon wafers) can become bent due to processing conditions. E.g. the stress of a spin-coater can kink a wafer.
====Material====
In principle, any substrate [[materials|material]] can be used. There are advantages to having a substrate material that has a larger critical angle than the film being studied:
# In [[reflectivity]], the region between the two critical angles will generate pseudo-waveguide modes, and provides a sensitive measure of film properties (e.g. [[absorption]]).
# In GISAXS, one can similarly take advantage of waveguide-like modes and intensity enhancements due to the strong reflection from the substrate.

====Substrate thickness====
Substrate thickness does not have any impact on GISAXS measurements. Thicker substrates can be advantageous in terms of maintaining rigorous substrate flatness (especially relevant for [[reflectivity]]); but even regular (0.5 mm thick) Si wafers are typically fine.
====Substrate coatings====
The substrate may have coatings without impacting measurements. Of course, any roughness introduced by intervening coatings will yield diffuse scattering. Moreover, the substrate layers will have different critical angles, which must be taken into account in interpreting data. But overall, substrate coatings are not problematic.
====Film coatings====
Generally, the thin film of interest is the outermost layer for GISAXS measurements. It is, however, possible to probe buried layers. Note, however, that one must consider the critical angles, and [[absorption lengths]] of layers placed on top of the film of interest. If the top layers are too thick/absorptive, then no signal will be measured. And, of course, to probe a buried layer one must be above the critical angle of all the superposed layers.
====Summary====
Despite these guidelines, in reality a wide variety of substrates are suitable. In practice, commercial single-crystal '''[[Material:Silicon|silicon]] wafers''' are an ideal substrate choice, as they are cheap, smooth, flat, and have well-defined surface chemistry. However even glass microscope slides will yield reasonable data, as well as other common substrates (e.g. [[Material:ITO|ITO]]).

===Dimensions===
A GISAXS beam is typically ~100 μm wide by ~50 μm tall. Because of the shallow grazing-incidence angle, the small beam height is nevertheless [[beam projection|projected]] into a large stripe; usually 1-12 mm long. As such, a stretched rectangle (microns wide by mm long) of the sample surface will be probed. In principle, samples as small as 0.5 mm × 0.5 mm can be measured (with a corresponding decrease in total scattering). On the other hand, samples as large as many inches can typically be accommodated. The ideal sample size is ~10 mm × ~10 mm. This size captures most of the x-ray beam, and makes alignment relatively simple and robust.

===Edge effects===
Note that the beam projection mentioned above means that a long stripe of the sample is being measured, including the edge of the substrate. Some film preparation methods may yield a different structure on the edge versus the center of the sample. For instance, spin-coating often generates a 'lip' of thicker material at the edge. In GISAXS, this thick region may in fact dominated the observed scattering signal (e.g. giving rise to a seemingly isotropic signal, even though the thin film region was anisotropic/aligned).

These effects can be mitigated by cleaving substrates to avoid edge effects, or by removing material near the edge (dabbing with a solvent-soaked swap, or simply using a razor blade). Edge effects are especially important in [[GTSAXS]], which specifically focuses on measuring the near-edge material.

===Structure===
Lastly, but most importantly, the sample must have some '''structure to be probed'''. A smooth and homogeneous film without any structure will not yield any scattering signal (other than an oscillation of specular intensity arising from the film thickness). A disordered film without any well-defined structure will yield [[diffuse scattering]], but nothing else. [[GISAXS]] is thus targeted at films that have well-defined nanostructure. ([[GIWAXS]] is targeted at films with well-defined molecular-scale structure.)

Material:Ethylene carbonate and diethyl carbonate

2014-06-23T14:01:59Z

130.199.3.165: /* Properties */

A mixture of:
* ethylene carbonate (C3H4O3, 1.32 g/cm3)
* diethyl carbonate (C5H10O3, 0.975 g/cm3)

==Properties==
{| class="wikitable"
|-
! Material
! density (g/cm3)
! X-ray energy (keV)
! X-ray wavelength (Å)
! critical angle (°)
! ''qc'' (Å−1)
! SLD (10−6Å−2)
|-
| 1:1 ethylene carbonate : diethyl carbonate
| 1.15
| 2.0
| 6.20
| 0.655
| 0.0232
| 10.70
|-
|
|
| 4.0
| 3.10
| 0.325
| 0.0230
| 10.52
|-
|
|
| 8.0
| 1.55
| 0.162
| 0.0229
| 10.43
|-
|
|
| 12.0
| 1.03
| 0.108
| 0.0229
| 10.41
|-
|
|
| 16.0
| 0.77
| 0.081
| 0.0229
| 10.40
|-
|
|
| 24.0
| 0.52
| 0.054
| 0.0229
| 10.39
|}

[[Image:Blend-ethyleneCarbonate-diethylCarbonate-atomic scatt factor.png|400px]][[Image:Blend-ethyleneCarbonate-diethylCarbonate-n.png|400px]]

[[Image:Blend-ethyleneCarbonate-diethylCarbonate-crit.png|400px]][[Image:Blend-ethyleneCarbonate-diethylCarbonate-crit_zoom.png|400px]]

[[Image:Blend-ethyleneCarbonate-diethylCarbonate-critq.png|400px]][[Image:Blend-ethyleneCarbonate-diethylCarbonate-SLD.png|400px]]

[[Image:Blend-ethyleneCarbonate-diethylCarbonate-AttLen.png|400px]][[Image:Blend-ethyleneCarbonate-diethylCarbonate-mu.png|400px]]

===X9 energy range===

[[Image:Blendzoom-ethyleneCarbonate-diethylCarbonate-AttLen.png|400px]][[Image:Blendzoom-ethyleneCarbonate-diethylCarbonate-mu.png|400px]]

Background

2014-06-20T19:35:24Z

130.199.3.165: /* Sources */

In [[scattering]], '''background''' refers to the unwanted scattering that arises from sources other than the sample of interest. It thus underlies the signal of interest, decreasing the [[GISAXS_measurement_time#Signal-to-noise_ratio|signal-to-noise ratio]], and making analysis more complicated.

==Sources==
# '''Detector''': Every detector has some background signal. The detector background may also have multiple components: a component that is present in every exposure (e.g. readout noise), as well as a component that scales with the exposure time (e.g. dark current). Detectors may also exhibit signal arises from other sources: e.g. cosmic rays, or even ambient light.
# '''Air scattering''': The incident beam, and scattered rays, will be scattered by ambient air that they travel through. This tends to broaden the beams (and thus peaks), and introduces diffuse background into the measurement. This source of background can be minimized by flushing the beam path with [[Material:Helium|helium]] gas (which has very weak scattering), or by pumping-down to near vacuum. Air scattering is most pronounced at lower [[x-ray energy|x-ray energies]]; it is nearly invisible for high-energy x-rays.
# '''Instrumental''': Most x-ray instruments will have windows that isolate the x-ray source (which is under vacuum) from the sample chamber. Even if the sample chamber is evacuated, x-ray transparent windows will likely remain in place. These windows (although nominally x-ray transparent) will give rise to a scattering signal. This scattering can be partially blocked using guard slits downstream of the window (ideally placed close to the sample). Even so, the low-''q'' scattering cannot be eliminated. Moreover, the slits will introduce some signal of their own (weak scattering; or bright streaks if they cut deeply into the incident beam). Windows placed after the sample (e.g. when the sample is in air but the downstream path is evacuated) will lead to scattering that cannot be eliminated. [[Material:Kapton|Kapton]] is frequently used; this material introduces diffuse low-''q'' scattering, as well as some weak halos at intermediate-''q''.
# '''Sample holder''': Especially in transmission-scattering experiments, the sample will typically be contained in a holder (e.g. a capillary, or between two Kapton sheets). This holder will of course introduce scattering.
# '''Matrix''': For materials that are dispersed (e.g. particles in solution or dispersed in a polymer), the matrix itself will lead to scattering.
# '''[[Diffuse scattering]]''': Confusingly, sometimes the diffuse scattering arising from the sample may also be referred to as a kind of background. The diffuse scattering generally arises from disorder: it may be considered an unwanted background when analyzing a structural peak; but it may be the signal of interest when analyzing heterogeneous ordering.

==Measuring==
One can attempt to measure the background, in preparation for subtracting it from the experimental data. A variety of measurements can be combined to assess the various sources of background.
* '''Dark signal''': By performing an exposure with the x-ray beam blocked, one can independently measure the '''detector''' component (#1) of the background.
* '''Direct beam''': By performing an exposure with the x-ray beam turned on, but without any sample (or even sample cell), one can measure the contributions from '''detector''', '''air scattering''', and '''instrumental''' (#1-3). The air+instrumental component can then be obtained by subtracting the dark signal from this direct beam measurement.
* '''Empty cell''': By measuring the empty sample cell, one additionally includes the '''sample holder'''; i.e. one measures #1-4.
* '''Empty cell (w/ matrix)''': One can instead measure an 'empty cell' where the '''matrix''' (e.g. solvent) is present; i.e. one measures #1-5.

==Subtraction==
===Full background subtraction===
In order to remove the effect of the background, the simplest solution is to simply measure it, and subtract it from the experimental data. However, there are a few issues to consider:
* '''Exposure time''': Most of the sources of background scale with exposure time. So a valid subtraction will require using the same exposure time for the background and sample measurements. In principle, one can do a more general background subtraction by rescaling the background and sample measurements by the exposure time; however if the detector has readout noise (which doesn't scale with exposure time), then this procedure is not valid. In such a case, one should get a separate measure of the readout noise ('''dark signal'''), and first subtract this from both images.
:<math>
I_{\mathrm{true}} = \frac{ (I_{\mathrm{sample}} - I_{\mathrm{readout}})/t_{\mathrm{sample}} }{ (I_{\mathrm{background}} - I_{\mathrm{readout}})/t_{\mathrm{background}} }
</math>
* '''Flux''': In fact, the exposure time is not the metric that matters: the total photon flux (over the course of the exposure) is what matters. I.e.: since a real-world x-ray beam does not have perfectly stable flux, it is better to normalize by the total photon flux during an exposure, rather than the total measurement time. This can be done if the [[beamline]]/instrument has a direct-beam monitor. (On some instruments, this is a non-blocking detector upstream of the sample; on others, the [[beamstop]] itself may be a photo-diode.)
:<math>
I_{\mathrm{true}} = \frac{ (I_{\mathrm{sample}} - I_{\mathrm{readout}})/\int \mathrm{flux}_{\mathrm{sample}} \mathrm{d}t }{ (I_{\mathrm{background}} - I_{\mathrm{readout}})/\int \mathrm{flux}_{\mathrm{background}} \mathrm{d}t }
</math>
* '''Shot noise''': As is true for any scattering measurement, the measurement of the background will have noise arising from finite counting statistics. This complicates background subtraction, since the noise is itself noisy. This can be minimized by using a very long exposure time for the background measurement ([[GISAXS_measurement_time#Mitigation|possibly split into multiple frames to avoid detector saturation]]). Doing so will mean the background has good signal-to-noise. However, one must then be careful in rescaling the background to compare it to the measurement of interest.

===Local background===
Although a full (2D image) background subtraction works quite well for transmission-[[SAXS]], it in general does not work for [[GISAXS]] or [[GIWAXS]]. This is because it is not possible to measure the 'empty cell' in a meaningful way. One might be tempted to do a [[GISAXS]] measurement on the bare substrate, and subtract this from the signal coming from the thin film. However, this will not work for a variety of reasons:
# The size of the bare substrate and the sample of interest are unlikely to be exactly matched (hence the total scattering will not be identical).
# The scattering from the substrate is modified by the presence of a sample layer on top of it: the reflection geometry modifies the intensity as well as the spatial distribution of scattering (e.g. [[refraction distortion]]). E.g. consider an extreme case where one is measuring below the [[critical angle]] of the sample film: the scattering of the substrate will be essentially absent.
# The sample film may also attenuate the substrate scattering due to [[absorption]] (the grazing-incidence geometry means that substrate scattering must travel a long path through the film; i.e. even relatively weak absorption will measurably affect the signal).
# The distinct [[dynamical scattering]] features of GISAXS ([[Yoneda]] streak, [[specular rod]], [[reflectivity oscillations]], etc.) are all influenced by the complete multi-layer stack (by the film/substrate density profile in the normal direction). Since these features are different in the background and sample measurements, a direct subtraction is not meaningful.
# The low-''q'' [[diffuse scattering]] is influenced by the roughness of interfaces (and scaled by the electron-density contrast across said interfaces). This is another example wherein the scattering of the substrate will be strongly modified by the presence of the sample film on top.
Thus, although one can subtract the detector and direct-beam backgrounds, one cannot hope to subtract the 'empty cell' (substrate) background; this latter background is likely to be dominant. An alternative strategy is to instead subtract a 'local background' when extracting a [[Tutorial:Linecuts|linecut]]. For instance, if assessing a peak position/width, one can fit the local data to a 'Gaussian + linear baseline' (or 'Gaussian + power-law baseline'), where the baseline is an (ad-hoc) accounting of the background. This inherently includes all the sources of background noted above.

In the case of an arc linecut (intensity along an arc at a constant ''q''), one can assess the 'local background' by taking a similar integration just outside the peak region, and subtracting the data from each corresponding angle. Alternatively, one can take ''q''-linecuts at each angle along the arc, and subtract an ad-hoc background as noted above.

Subtracting a local background inherently includes all sources of background scattering noted above. This works well for well-defined structural peaks, where the contributions from the peak and the baseline can be easily identified. For diffuse scattering or even broad halos, this may not be possible.

Example:P3HT orientation analysis

2014-06-20T19:25:49Z

130.199.3.165: /* Step 1: Conversion to q-space */

This tutorial describes how to quantify the orientation distribution of the semiconducting polymer [[P3HT]] using [[GIWAXS]]. This orientation analysis is meant to determine the relative amounts of the material oriented in different ways. The same kind of analysis can be applied to other semiconducting polymers or small-molecules. In fact, the same conceptual steps can be applied more broadly to determining any kind of orientation distribution (though one must be careful in interpreting the relationship between [[reciprocal-space]] peaks, which will be different for each material's specific [[unit cell]]).

==P3HT orientation==
P3HT crystallizes into the [[unit cell]] shown below. P3HT crystals are anisotropic, often appearing as long needle-like structures. Note that this unit cell is highly idealized: the alkyl side-chains have considerable freedom and thus disorder (they may even be liquid-like). Moreover, real samples of P3HT organize in a more disordered state than shown here. Although the lamellar stacking is well-defined, and the aromatic (''π''-''π'') stacking is also well-defined, one typically does not observe any scattering peak along the backbone direction: i.e. there is usually no well-defined persistence of order in this direction. It is also likely that subsequent chains do not organize with the well-defined registry shown in the cartoon. Overall, P3HT is thus better thought of as being semi-crystalline or liquid-crystalline: it exhibits considerable molecular order (giving rise to scattering peaks), but is not an extended well-ordered crystal.
[[Image:Cell3-main2.png|thumb|center|300px|Cartoon of an idealized P3HT [[unit cell]].]]
* The lamellar stacking has a spacing of ~1.6 nm, [[Q value|giving rise]] to a peak (100) at ''q'' ~0.4 Å−1.
* The aromatic (''π''-''π'') stacking has a spacing of ~0.39 nm, [[Q value|giving rise]] to a peak (010) at ''q'' ~1.6 Å−1.
* The spacing along the ring direction is too disordered to give a well-defined 001 peak.

When P3HT is cast as a thin-film, this unit cell can adopt a variety of orientations. Although most materials form 3D powders when cast from solution, P3HT adopts a relatively well-defined orientation with respect to the substrate. It seems that the alkyl side-chains preferentially segregate to the film-air and film-substrate interfaces (presumably in order to lower the interfacial energy), which drives the material overall into the ''edge-on'' orientation shown below:

{|
| [[Image:Cell3-edge on2.png|200px|thumb|edge-on]]
| [[Image:Cell3-face on2.png|200px|thumb|face-on]]
| [[Image:Cell3-end on2.png|200px|thumb|end-on]]
|}

Absent any other driving force, the above configurations are assumed to be in-plane isotropic (2D powders). In such a case, one would expect to see [[reciprocal-space]]s corresponding to these states of:

{|
| [[Image:P3ht_rs-edge-on.png|200px|thumb|edge-on]]
| [[Image:P3ht_rs-face-on.png|200px|thumb|face-on]]
| [[Image:P3ht_rs-end-on.png|200px|thumb|end-on]]
| [[Image:P3ht_rs-powder.png|200px|thumb|isotropic]]
|}

Of course, what one observes on the detector is only where the [[Ewald sphere]] intersects [[reciprocal-space]]:

{|
| [[Image:P3ht_det-edge-on.png|200px|thumb|edge-on]]
| [[Image:P3ht_det-face-on.png|200px|thumb|face-on]]
| [[Image:P3ht_det-end-on.png|200px|thumb|end-on]]
| [[Image:P3ht_det-powder.png|200px|thumb|isotropic]]
|}

Summarizing:
* '''Edge-on''' involves the lamellar side-chains wetting the interfaces, which means the lamellar stacking is vertical (100 peak along ''qz''), and the ''π''-''π'' stacking is then in-plane (010 peak along ''qr'').
* '''Face-on''' involves the aromatic rings facing the substrate, which means the lamellar stacking is in-plane (100 peak along ''qr''), and the ''π''-''π'' stacking is in the film normal direction (010 peak along ''qz'').
* '''End-on''' involves the chain ends pointing towards, which means the lamellar stacking is in-plane (100 peak along ''qr''), and the ''π''-''π'' stacking is also in-plane (010 peak along ''qr''). Since the chain axis doesn't give a well-defined peak, there is no scattering along ''qz''.
* '''Isotropic''' involves a complete orientational averaging of the unit cell orientation. The lamellar (100) peak and the ''π''-''π'' (010) peak will both appear to be rings of uniform intensity.

==Example GIWAXS==
Shown below is a typical [[GIWAXS]] image of P3HT cast on a [[Material:Silicon|silicon]] substrate:

[[Image:P3ht-generic giwaxs02.png|450px|center]]

Because of the ''edge-on'' orientation, the lamellar peaks appear along the ''qz'' axis. Below is a comparison of P3HT with different orientation distributions.

{|
| [[Image:P3ht-generic giwaxs.png|300px|center|thumb|[[Material:P3HT|P3HT]] with predominantly '''edge-on''' orientation. The 100 peak is along ''qz'', while the 010 peak is along ''qx''.]]
| [[Image:P3ht-face-on giwaxs.png|300px|center|thumb|P3HT with predominantly '''face-on''' orientation. Notice the 100 peak is along ''qx'', while a weak 010 peak can be seen near the ''qz'' axis.]]
| [[Image:P3ht-isotropic giwaxs.png|300px|center|thumb|P3HT with nearly '''isotropic''' orientation. Notice the extremely broad (nearly uniform) distribution of intensity for all the peaks.]]
|}

==Analysis: In-plane powder==
In order to quantify the orientation distribution of P3HT, we need to measure the intensity of the scattering as a function of angle. We define the azimuthal angle to be ''χ'': this is the angle with respect to the ''qz'' axis. I.e. ''χ'' = 0° is the out-of-plane (''qz'') axis, while ''χ'' = 90° is the in-plane (''qr'') axis.
===Step 1: Conversion to ''q''-space===
The raw detector image needs to be converted into [[reciprocal-space]]. This is typically done by using a [[Materials#Calibration_standards|calibration standard]], which has rings at known ''q''-position. The purpose of calibration is to convert from pixel position to <math>(q_x,q_z)</math> value. One needs to know:
# The [[X-ray energy|x-ray wavelength]]. This is known since it is set by the x-ray source (and/or monochromator).
# The unitless detector distance D/d, where D is the detector distance and d is the detector width. Since d is typically known, one can either measure D directly (even using a tape measure is reasonable accurate), or by noting the pixel position of a ring in calibration standard.
# Direct beam position (i.e. the pixel position of the direct beam). Even with the beam block by a beamstop, low-''q'' beam spillover is usually sufficient to note the beam position. One can also determine the center of scattering rings to define the beam position.
# Detector tilt. This can be assessed by noting the curvature of scattering rings from a standard sample.
With the above information, one can convert from the raw image into data in [[reciprocal-space]] (various pieces of [[software]] will do this for you).

Notice that one can either display the data as <math>(q_x,q_z)</math> or as <math>(q_r,q_z)</math>, where:
:<math>
q_r = \sqrt{ q_x^2 + q_y^2 }
</math>
The <math>(q_x,q_z)</math> representation ignores the ''qy'' component of the [[momentum transfer]]. For small-angle measurements ([[GISAXS]]), this is a reasonable approximation. However for wide-angle ([[GIWAXS]]) measurements, this is a poor approximation: the curvature of the [[Ewald sphere]] means that the part of reciprocal-space probed by the detector is curving away from the <math>(q_x,q_z)</math> plane. As such, in the <math>(q_r,q_z)</math> representation, we note a 'missing wedge' of data near the ''qz'' axis. In fact, in grazing-incidence geometry, we do not probe the ''true'' ''qz'' axis, except at two points (the direct beam position, and the specularly-reflected beam position).

{|
| [[Image:P3ht calibration01.png|thumb|250px|Raw detector image.]]
| [[Image:P3ht calibration02.png|thumb|300px|Data converted to ''q''-space.]]
| [[Image:P3ht calibration03.png|thumb|300px|Data converted to ''q''-space, taking into account the [[Ewald sphere]].]]
|}

The conversion to ''q''-space is necessary for all subsequent analysis steps. Moreover, we typically are interested in ''χ'' defined in [[reciprocal-space]] (i.e. with respect to the sample coordinates, not the instrument reference frame), so we should compute ''χ'' in the <math>(q_r,q_z)</math> representation shown above.

===Step 2: Linecut===
From the converted data, we can take a linecut along a ''χ''-arc. In the present analysis, the most useful place to take such a cut is along the 100 lamellar peak (and then along the 010 aromatic stacking peak). When taking the linecut, one should consider:
# When extracting the intensities along the arc, one should try to integrate the full peak width. The integration must be wide enough to take the full peak into account for all ''χ'' (otherwise the intensity will change along ''χ'' simply due to the fraction of the peak one is probing.
# The intensity data should be [[background]]-subtracted. In this case, subtracting the [[Background#Local_background|local background]] makes the most sense: i.e. subtract the intensity just outside the arc of interest. (This must be done at each corresponding ''χ'', since the background may not be isotropic.)
# The ''χ''-scale should be shifted in order to take into account the above-noted curvature of the Ewald sphere. Thus, there will be a small gap in the data near ''χ'' = 0°.
# One should ignore the [[Yoneda]] streak, since it exhibits an intensity enhancement. Any data at ''χ'' beyond the Yoneda should also be discarded since this data comes from below the [[horizon]], and is thus attenuated. For the P3HT 100 peak, this usually means eliminating ''χ'' > ~82°.
# In principle, one should re-adjust the ''χ''-scale to take into account [[refraction distortion]]s: the grazing-incidence geometry induces substantial beam refractions, which causes [[reciprocal-space]] to look warped on the detector image. This distortion only affects the ''qz'' component, and is greatest near the Yoneda. This distortion is substantial in [[GISAXS]], but is usually negligible in [[GIWAXS]].

[[Image:P3ht chi example.png|400px|thumb|center|Example of integrated peak intensity along ''χ''-arcs for an edge-on P3HT sample. The dark line is the lamellar 100 peak, the grey line is the aromatic 010 peak.]]

===Step 3: Account for sample symmetry===
The ''I'' vs. ''χ'' curve shown above can be thought of as the orientation distribution of the P3HT. However, one must be careful in directly interpreting the intensity as representing the ''amount of material''. The reason for this (as usual) is that the [[Ewald sphere]] is probing only a single slice through the 3D reciprocal-space. So we are not probing the full scattering intensity for any given population.

How to properly account for the full scattering intensity depends on sample symmetry. In the most general sense, we can rotate the sample, accumulate multiple images, and reconstruct the full 3D reciprocal-space. However, it is far easier to account for this mathematically, if we know the sample symmetry. It turns out, that for an in-plane powder, we must simply multiply the above curve by <math>\sin(\chi)</math>. For a detailed explanation of why this is the case, refer to [[Integrated intensity|integrated intensity]]. Roughly, this factor arises from the spherical coordinate system, aligned with the symmetry axis of the 2D powder. More heuristically, one can imagine that observed scattering intensity near ''qr'' actually represents a whole ring of scattering in the 3D reciprocal-space. This 'ring' becomes smaller at larger ''χ''; the <math>\sin(\chi)</math> factor exactly accounts for this variation.

{|
| [[Image:p3ht_chi_example02.png|350px]]
| [[Image:p3ht_chi_example03.png|350px]]
|}

The corrected data (right panel above) now has the intensity being proportional to the ''amount of material'' oriented at that ''χ'' angle. This curve can be reported as an orientation distribution for the material (closely related to [[pole figures]]).

===Step 4: Integrate populations===
One can now integrate the intensity in the corrected curve, to come up with estimates of the relative amount of material. There are many ways one could choose to do this. In this example, we divide the scattering intensity into three populations:
* '''Isotropic''': The scattering intensity arising from the subset of grains that form an isotropic distribution.
* '''Edge-on''': The scattering intensity arising from the edge-on grains. We include all grains with an orientation χ<45°.
* '''Face-on''': The scattering intensity arising from the face-on grains. We include all grains with an orientation χ>45°.

Note that we are here assuming that all the intensity from the 100 scattering along ''qr'' arises from entirely from ''face-on'' material. However, both ''face-on'' and ''end-on'' material would give rise to scattering at that position in [[reciprocal-space]]. To differentiate between those two possibilities, one must invoke additional data. Specifically, one can look at the 010 (''π''-''π'') peak: for ''end-on'', the ''π''-''π'' peak will also be in-plane (along ''qr''), whereas for ''face-on'', one should observe substantial intensity of the ''π''-''π'' peak in the out-of-plane direction (near ''qz'' axis).

For the present example, the ''end-on'' orientation was excluded as a possibility, and therefore we ascribe all of the ''qr'' scattering to the ''face-on'' orientation. We compute integrated quantities by summing up the area under the curve, and distributing it into the three categories noted above. Importantly, the isotropic population appears as a uniform baseline (isotropic ring) in the original data, and thus appears as a <math>\sin(\chi)</math> baseline in the corrected data.

{|
| [[Image:Pop schematict03.png|300px|]]
| [[Image:Pop schematict04b.png|300px|]]
|}

Note again that only the intensities in the corrected curve (right panel above) are linearly representative of the ''amount of material''. We can compare the three integrated values to the total, and thereby compute a percentage for edge-on, face-on, and isotropic.

==Analysis: In-plane aligned==
Note that for a sample that ''isn't'' an in-plane powder (e.g. P3HT aligned in a grating), then the above symmetry arguments would change. In that case, one would need to instead account for the orientation distribution in the in-plane direction (''ϕ''). Note that if the material were highly aligned with the grating axis ((''ϕ'' = 0°), then a single measurement in this aligned geometry would be sufficient to assess the full orientation distribution. In other words, the original uncorrected data would correctly represent the relative amounts of material:

[[Image:Pop schematict03.png|300px|]]

See also [[grating alignment]] for caveats related to the in-plane angle (''ϕ'').

==Literature==

===Development/description of analysis method===
* [http://pubs.acs.org/doi/abs/10.1021/nn202515z Nanoimprint-Induced Molecular Orientation in Semiconducting Polymer Nanostructures] Htay Hlaing, Xinhui Lu, Tommy Hofmann, [[Kevin Yager|Kevin G. Yager]], Charles T. Black, and Benjamin M. Ocko ''ACS Nano'' 2011, 5 (9), 7532-7538 [http://dx.doi.org/10.1021/nn202515z doi: 10.1021/nn202515z]
* [http://scitation.aip.org/content/aip/journal/apl/99/16/10.1063/1.3651509 Enhanced charge collection in confined bulk heterojunction organic solar cells] Jonathan E. Allen, [[Kevin G. Yager]], Htay Hlaing, Chang-Yong Nam, Benjamin M. Ocko and Charles T. Black ''Applied Physics Letters'' 2011, 99, 163301. [http://dx.doi.org/10.1063/1.3651509 doi: 10.1063/1.3651509] '''c.f. [ftp://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-99-015142/080111_TemplatedOrganicSolarCells_SupplementaryInformation_APL_final.pdf Supplementary Information]'''
* [http://pubs.acs.org/doi/abs/10.1021/nl301759j One-Volt Operation of High-Current Vertical Channel Polymer Semiconductor Field-Effect Transistors] Johnston, D.E.; [[Kevin Yager|Yager, K.G.]]; Nam, C.-Y.; Ocko, B.M.; Black, C.T. ''Nano Letters'' 2012, 8, 4181–4186 [http://dx.doi.org/10.1021/nl301759j doi: 10.1021/nl301759j]
* '''[http://pubs.acs.org/doi/abs/10.1021/nn4060539 Nanostructured Surfaces Frustrate Polymer Semiconductor Molecular Orientation]''' Johnston, D.E.; [[Kevin Yager|Yager, K.G.]]; Hlaing, H.; Lu, X.; Ocko, B.M.; Black, C.T. ''ACS Nano'' 2014 [http://dx.doi.org/10.1021/nn4060539 doi: 10.1021/nn4060539]

===Application of method===
* [http://pubs.acs.org/doi/abs/10.1021/cm501251n Stable and Controllable Polymer/Fullerene Composite Nanofibers through Cooperative Noncovalent Interactions for Organic Photovoltaics] Fei Li, [[Kevin G. Yager]], Noel M. Dawson, Ying-Bing Jiang, Kevin J. Malloy, and Yang Qin ''Chemistry of Materials'' 2014 [http://dx.doi.org/10.1021/cm501251n doi: 10.1021/cm501251n]
===Related papers===
====Angular correction (curvature of [[Ewald sphere]])====
* '''[http://pubs.acs.org/doi/abs/10.1021/la904840q Quantification of Thin Film Crystallographic Orientation Using X-ray Diffraction with an Area Detector]''' Jessy L. Baker, Leslie H. Jimison, Stefan Mannsfeld, Steven Volkman, Shong Yin, Vivek Subramanian, Alberto Salleo, A. Paul Alivisatos and Michael F. Toney ''Langmuir'' 2010, 26 (11), 9146-9151. [http://dx.doi.org/10.1021/la904840q doi: 10.1021/la904840q]
* [http://scripts.iucr.org/cgi-bin/paper?S0021889808001064 Simulating X-ray diffraction of textured films] D. W. Breiby, O. Bunk, J. W. Andreasen, H. T. Lemke and M. M. Nielsen ''J. Appl. Cryst.'' 2008, 41, 262-271. [http://dx.doi.org/10.1107/S0021889808001064 doi: 10.1107/S0021889808001064]
====sin(angle) correction====
* [http://pubs.acs.org/doi/abs/10.1021/nl501233g Confinement-Driven Increase in Ionomer Thin-Film Modulus] Kirt A. Page, Ahmet Kusoglu, Christopher M. Stafford, Sangcheol Kim, R. Joseph Kline, and Adam Z. Weber ''Nano Letters'' 2014, 14 (5), 2299-2304. [http://dx.doi.org/10.1021/nl501233g doi: 10.1021/nl501233g]
====Other orientation analyses====
* [http://scripts.iucr.org/cgi-bin/paper?S0021889806038957 Evaluation of equatorial orientation distributions] C. Burger and W. Ruland ''J. Appl. Cryst.'' 2006, 39, 889-891. [http://dx.doi.org/10.1107/S0021889806038957 doi: 10.1107/S0021889806038957]
* [http://scripts.iucr.org/cgi-bin/paper?S0021889807010503 Two-dimensional small-angle X-ray scattering of self-assembled nanocomposite films with oriented arrays of spheres: determination of lattice type, preferred orientation, deformation and imperfection] W. Ruland and B. M. Smarsly ''J. Appl. Cryst.'' 2007, 40, 409-417. [http://dx.doi.org/10.1107/S0021889807010503 doi: 10.1107/S0021889807010503]
* [http://pubs.acs.org/doi/abs/10.1021/nl903187v Device-Scale Perpendicular Alignment of Colloidal Nanorods] Jessy L. Baker, Asaph Widmer-Cooper, Michael F. Toney, Phillip L. Geissler and A. Paul Alivisatos ''Nano Letters'' 2010, 10 (1), 195-201. [http://dx.doi.org/10.1021/nl903187v doi: 10.1021/nl903187v]

Tutorial:Qualitative inspection

2014-06-20T15:17:05Z

130.199.3.165: /* Scattering Intensity */

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.

==Amount of Order==
====No Scattering====
A lack of scattering signal is a good indicator that the sample lacks any kind of well-defined structure (at least in the size-scales being probed by the available ''[[Q value|q]]''-range). Of course, one must be careful to eliminate other possibilities: sample misaligned, beam flux too low, etc. A particular pathological possibility is that the sample is actually extremely well-ordered (e.g. single crystal), but just happens to be in an alignment where none of the [[reciprocal-space]] peaks are on the detector.

====Diffuse Scattering====
TBD

====Single Broad Ring (Halo)====
TBD

====Multiple Rings====
TBD

====Multiple Sharp Rings====
TBD

====Multiple Sharp Peaks====
TBD

==Peak Position==
The position of a peak in [[GISAXS]] allows one to infer the sizescale of the realspace ordering. Recall that [[reciprocal-space]] is inverted: i.e. peaks at large angle (large ''q'') [[Q value|correspond]] to small-scale structures; whereas peaks at small angle (small ''q'') correspond to larger (nanoscale) structures. Ultrasmall angle scattering ([[USAXS]]) probes yet larger (micron-scale) order. More specifically, when observing peaks at:
* Very large angle (0.5-4 Å−1): Atomic packing distances (1-10 Å).
* Large angle (0.2-2 Å−1): Molecular packing distances (0.3-3 nm). For instance, aromatic rings tend to pi-pi stack with a 0.3-0.4 nm repeat distance.
* Medium angle (0.03-0.3 Å−1): Macromolecular distances (2-20 nm). For instance, polymers often crystallize into chain-folded lamellae with a period of 2-10 nm.
* Small angle (0.0002-0.04 Å−1): Nanoscale distances (15-300 nm). For instance, block-copolymers and nanoparticle [[superlattice]]s tend to organize in this size regime.
* Ultra-small angle (<0.0006 Å−1): Micron sizes (>1 µm).

==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==
The total scattering intensity one observes on the detector is affected by a number of factors. The scattering intensity of course influences the [[GISAXS_measurement_time#Factors_affecting_exposure_time|time required for taking a measurement]].

===Flux===
Obviously, the observed scattering intensity is depending on beam flux. A high-flux beam will yield a correspondingly higher number of counts/second than a lower-flux beam. So, when comparing scattering intensities, one must account for the beam flux, and the measurement time.

===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).

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]]).

===Amount of Material===
For a given scattering volume, the intensity of the scattering can be thought of as a probe of the fraction of the material in the given state/phase/configuration. I.e. if a given peak is stronger in one sample vs. another, then this means that the phase (crystal form, etc.) corresponding to that peak appears more frequently in that sample. One must be careful, however, as many other things are implicated in peak heights (orientation, disorder, etc.).

===Order===
Note that in general, well-ordered systems will appear to scatter more strongly than weakly-ordered systems. A broad scattering peak (small grains) will have lower maximum intensity than a sharp scattering peak (big grains). More generally, periodically ordered structures give rise to scattering events, whereas homogeneous systems do not scattering the incident radiation.

===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]]).

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).

==Higher Orders==
Higher-order peaks in x-ray scattering generally imply a well-defined structure. Qualitatively, if you see lots of higher-orders, you can say you have a very well-organized structure. For molecular peaks, this usually means a high-quality crystal (with large [[Scherrer grain size analysis|grain sizes]]). For nanoscale peaks, this usually means a well-defined [[superlattice]] of some kind.

Conversely, disorder tends to broaden peaks, and also extinguish the intensity of higher-order peaks (c.f. [[Debye-Waller factor]]). Observing only a single peak means a highly disordered system (e.g. amorphous packing); i.e. there is some preferred particle-particle distance, but no recognizable [[lattice]] order to longer distances.

==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.

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.

For instance, consider a lamellar structure with total layer spacing ''d''; of course we [[Q value|expect]] [[reciprocal-space]] peaks at |''q''| = 2 ''π''/''d'', and in fact we expect higher-orders at |''q''| = ''n'' 2 ''π''/''d'' for all integer ''n''. However, for a well-defined two-layer structure where each sub-layer has the same thickness (square-wave density profile), the even-order reflections will be absent. If the two sub-layers have different thicknesses, then the even-order peaks will be present. More generally, the variation in intensity between the odd and even peaks can be used to deduce the duty-cycle.

On the other extreme, consider a 1D repeating structure where the density varies sinusoidally; the higher odd orders will be absent. In fact, a perfectly sinusoidal structure only needs the fundamental [[Fourier transform|Fourier]] component to completely describe the density-profile. In other words, the higher-order peaks will be entirely absent.

==Orientation Distribution==
TBD

==Crystal Order and Orientation==
TBD (amorphous, 3D powder, in-plane powder, single-crystal)

Labscale

2014-06-20T15:13:02Z

130.199.3.165:

The term '''labscale''' is informally used to refer to small-scale [[x-ray]] instruments used for diffraction or [[scattering]], in comparison to [[synchrotron]] [[beamlines]].

Labscale instruments typically use a rotating anode as an x-ray source. Their flux is much lower than a synchrotron (which is 3-6 orders-of-magnitude brighter). Labscale instruments also typically haver larger beam sizes, worse resolution, and lower coherence. Nevertheless, useful data can be obtained on many systems, especially [[Tutorial:Qualitative_inspection#Scattering_Intensity|strongly scattering]] samples.

Labscale

2014-06-20T15:04:55Z

130.199.3.165: Created page with "The term '''labscale''' is informally used to refer to small-scale x-ray instruments, in comparison to synchrotron beamlines. Labscale instruments typically use a..."

The term '''labscale''' is informally used to refer to small-scale [[x-ray]] instruments, in comparison to [[synchrotron]] [[beamlines]].

Labscale instruments typically use a rotating anode as an x-ray source. Their flux is much lower than a synchrotron (which is 3-6 orders-of-magnitude brighter). Labscale instruments also typically haver larger beam sizes, worse resolution, and lower coherence. Nevertheless, useful data can be obtained on many systems, especially strongly [[scattering]] samples.

Beamlines

2014-06-20T15:02:43Z

130.199.3.165:

The following is a list of [[x-ray]] [[scattering]] [[beamline]]s available to the user community:

==Available Synchrotron Beamlines==

{| class="wikitable"
|-
! Beamline
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[X9]]'''
| [[NSLS]] at [[BNL]]
| Running until Sept. 2014
| [[X9]] is an undulator-based (high-flux) and high-resolution beamline that can perform transmission and grazing-incidence scattering across a wide ''q''-range (simultaneous SAXS/WAXS possible). Typical beam size is 150 µm for TSAXS and 50 µm for GISAXS (focus to ~15 µm is possible). Measurements in air or vaccum are possible. Sample environments for performing in-situ sample heating (RT-220°C for GISAXS, RT-80°C for TSAXS) are available. Accomodations for in-situ experiments (solvent annealing, electrochemical cells) are also possible. Contact [http://staff.ps.bnl.gov/staff.aspx?id=21212 Lin Yang], [http://staff.ps.bnl.gov/staff.aspx?id=10076 Masa Fukuto], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 6 keV to 20 keV
| 0.002 Å−1 to 4.2 Å−1
| Through [http://www.bnl.gov/ps/nsls/users/access/beamtime-new_users.asp NSLS] or [http://www.bnl.gov/cfn/user/ CFN] user programs. (No longer accepting proposals.)
|-
|-
| '''[[7.3.3]]'''
| [http://www-als.lbl.gov/index.php/beamlines/beamlines-directory.html ALS] at [http://www.lbl.gov/ LBNL]
| Running
| [[7.3.3]] is a SAXS/WAXS/GISAXS/GIWAXS beamline, covering a wide ''q'' range (0.004 - 2.5 Å−1) and length scale (2.5 - 1500 angstrom). See more details at [http://www-als.lbl.gov/index.php/beamlines/beamlines-directory.html ALS website]. New users, please contact Alex Hexemer, Eric Schaible, or Chenhui Zhu for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 10 keV
| 0.004 Å−1 to 2 Å−1
| General user program. [http://www-als.lbl.gov/index.php/contact/701-rapidd-proposals.html Rapid access is also available].
|-
|}

==Available Labscale Instruments==
{| class="wikitable"
|-
! Instrument
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[CFN Bruker Nanostar|Bruker Nanostar]]'''
| [[CFN]] at [[BNL]]
| Running
| This [[labscale]] rotating-anode instrument is available to users. Of course a labscale instrument will not have the flux or resolution of a synchrotron beamline; nevertheless this instrument is optimized for resolution, while providing sufficient flux for measuring strongly scattering systems (e.g. nanoparticles). The sample environment is under vacuum, and offers both transmission-mode and grazing-incidence stages. Contact [http://www.bnl.gov/cfn/people/staff.php?q=124 Dmytro Nykypanchuk] or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| [[Cu K-alpha|8.04 keV]]
| 0.005 Å−1 to 0.3 Å−1 (up to ~2 Å−1 using image plate).
| Available through [http://www.bnl.gov/cfn/user/ CFN user program].
|-
|}

==Future Synchrotron Beamlines==
{| class="wikitable"
|-
! Beamline
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[CMS]]'''
| [[NSLS-II]] at [[BNL]]
| Under construction.
| [[CMS]] is an bending-magnet beamline being constructed at [[NSLS-II]], based in part on the design and hardware at [[X9]] ([[NSLS]]). The beamline will be able to perform transmission and grazing-incidence scattering across a wide ''q''-range (simultaneous SAXS/WAXS possible), and will emphasize automation, high-throughput, and in-situ measurements. Contact [http://staff.ps.bnl.gov/staff.aspx?id=10076 Masa Fukuto], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 10 keV to 17 keV
| 0.002 Å−1 to 4.2 Å−1
| Will be available through NSLS-II user program.
|-
| '''[[SMI]]'''
| [[NSLS-II]] at [[BNL]]
| Under construction.
| [[SMI]] is a undulator-based beamline being constructed at [[NSLS-II]]. SMI will be a high-flux and high-resolution instrument optimized for grazing-incidence measurements on interfaces, though also capable of performing world-class transmission scattering experiments. [http://staff.ps.bnl.gov/staff.aspx?id=20298 Elaine DiMasi], [http://staff.ps.bnl.gov/staff.aspx?id=83687 Mikhail Zhernenkov], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]], [[XR]]
| ~2 keV to 24 keV
| Very wide ''q''-range (SAXS and WAXS).
| Will be available through NSLS-II user program.
|-
|}

Beamlines

2014-06-20T14:58:45Z

130.199.3.165:

The following is a list of [[x-ray]] [[scattering]] [[beamlines]] available to the user community:

==Available Synchrotron Beamlines==

{| class="wikitable"
|-
! Beamline
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[X9]]'''
| [[NSLS]] at [[BNL]]
| Running until Sept. 2014
| [[X9]] is an undulator-based (high-flux) and high-resolution beamline that can perform transmission and grazing-incidence scattering across a wide ''q''-range (simultaneous SAXS/WAXS possible). Typical beam size is 150 µm for TSAXS and 50 µm for GISAXS (focus to ~15 µm is possible). Measurements in air or vaccum are possible. Sample environments for performing in-situ sample heating (RT-220°C for GISAXS, RT-80°C for TSAXS) are available. Accomodations for in-situ experiments (solvent annealing, electrochemical cells) are also possible. Contact [http://staff.ps.bnl.gov/staff.aspx?id=21212 Lin Yang], [http://staff.ps.bnl.gov/staff.aspx?id=10076 Masa Fukuto], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 6 keV to 20 keV
| 0.002 Å−1 to 4.2 Å−1
| Through [http://www.bnl.gov/ps/nsls/users/access/beamtime-new_users.asp NSLS] or [http://www.bnl.gov/cfn/user/ CFN] user programs. (No longer accepting proposals.)
|-
|-
| '''[[7.3.3]]'''
| [http://www-als.lbl.gov/index.php/beamlines/beamlines-directory.html ALS] at [http://www.lbl.gov/ LBNL]
| Running
| [[7.3.3]] is a SAXS/WAXS/GISAXS/GIWAXS beamline, covering a wide ''q'' range (0.004 - 2.5 Å−1) and length scale (2.5 - 1500 angstrom). See more details at [http://www-als.lbl.gov/index.php/beamlines/beamlines-directory.html ALS website]. New users, please contact Alex Hexemer, Eric Schaible, or Chenhui Zhu for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 10 keV
| 0.004 Å−1 to 2 Å−1
| General user program. [http://www-als.lbl.gov/index.php/contact/701-rapidd-proposals.html Rapid access is also available].
|-
|}

==Available Labscale Instruments==
{| class="wikitable"
|-
! Instrument
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[CFN Bruker Nanostar|Bruker Nanostar]]'''
| [[CFN]] at [[BNL]]
| Running
| This [[labscale]] rotating-anode instrument is available to users. Of course a labscale instrument will not have the flux or resolution of a synchrotron beamline; nevertheless this instrument is optimized for resolution, while providing sufficient flux for measuring strongly scattering systems (e.g. nanoparticles). The sample environment is under vacuum, and offers both transmission-mode and grazing-incidence stages. Contact [http://www.bnl.gov/cfn/people/staff.php?q=124 Dmytro Nykypanchuk] or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| [[Cu K-alpha|8.04 keV]]
| 0.005 Å−1 to 0.3 Å−1 (up to ~2 Å−1 using image plate).
| Available through [http://www.bnl.gov/cfn/user/ CFN user program].
|-
|}

==Future Synchrotron Beamlines==
{| class="wikitable"
|-
! Beamline
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[CMS]]'''
| [[NSLS-II]] at [[BNL]]
| Under construction.
| [[CMS]] is an bending-magnet beamline being constructed at [[NSLS-II]], based in part on the design and hardware at [[X9]] ([[NSLS]]). The beamline will be able to perform transmission and grazing-incidence scattering across a wide ''q''-range (simultaneous SAXS/WAXS possible), and will emphasize automation, high-throughput, and in-situ measurements. Contact [http://staff.ps.bnl.gov/staff.aspx?id=10076 Masa Fukuto], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 10 keV to 17 keV
| 0.002 Å−1 to 4.2 Å−1
| Will be available through NSLS-II user program.
|-
| '''[[SMI]]'''
| [[NSLS-II]] at [[BNL]]
| Under construction.
| [[SMI]] is a undulator-based beamline being constructed at [[NSLS-II]]. SMI will be a high-flux and high-resolution instrument optimized for grazing-incidence measurements on interfaces, though also capable of performing world-class transmission scattering experiments. [http://staff.ps.bnl.gov/staff.aspx?id=20298 Elaine DiMasi], [http://staff.ps.bnl.gov/staff.aspx?id=83687 Mikhail Zhernenkov], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]], [[XR]]
| ~2 keV to 24 keV
| Very wide ''q''-range (SAXS and WAXS).
| Will be available through NSLS-II user program.
|-
|}

Beamlines

2014-06-20T14:55:32Z

130.199.3.165: /* Available Labscale Instruments */

The following is a list of x-ray scattering beamlines available to the user community:

==Available Synchrotron Beamlines==

{| class="wikitable"
|-
! Beamline
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[X9]]'''
| [[NSLS]] at [[BNL]]
| Running until Sept. 2014
| [[X9]] is an undulator-based (high-flux) and high-resolution beamline that can perform transmission and grazing-incidence scattering across a wide ''q''-range (simultaneous SAXS/WAXS possible). Typical beam size is 150 µm for TSAXS and 50 µm for GISAXS (focus to ~15 µm is possible). Measurements in air or vaccum are possible. Sample environments for performing in-situ sample heating (RT-220°C for GISAXS, RT-80°C for TSAXS) are available. Accomodations for in-situ experiments (solvent annealing, electrochemical cells) are also possible. Contact [http://staff.ps.bnl.gov/staff.aspx?id=21212 Lin Yang], [http://staff.ps.bnl.gov/staff.aspx?id=10076 Masa Fukuto], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 6 keV to 20 keV
| 0.002 Å−1 to 4.2 Å−1
| Through [http://www.bnl.gov/ps/nsls/users/access/beamtime-new_users.asp NSLS] or [http://www.bnl.gov/cfn/user/ CFN] user programs. (No longer accepting proposals.)
|-
|-
| '''[[7.3.3]]'''
| [http://www-als.lbl.gov/index.php/beamlines/beamlines-directory.html ALS] at [http://www.lbl.gov/ LBNL]
| Running
| [[7.3.3]] is a SAXS/WAXS/GISAXS/GIWAXS beamline, covering a wide ''q'' range (0.004 - 2.5 Å−1) and length scale (2.5 - 1500 angstrom). See more details at [http://www-als.lbl.gov/index.php/beamlines/beamlines-directory.html ALS website]. New users, please contact Alex Hexemer, Eric Schaible, or Chenhui Zhu for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 10 keV
| 0.004 Å−1 to 2 Å−1
| General user program. [http://www-als.lbl.gov/index.php/contact/701-rapidd-proposals.html Rapid access is also available].
|-
|}

==Available Labscale Instruments==
{| class="wikitable"
|-
! Instrument
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[CFN Bruker Nanostar|Bruker Nanostar]]'''
| [[CFN]] at [[BNL]]
| Running
| This [[labscale]] rotating-anode instrument is available to users. Of course a labscale instrument will not have the flux or resolution of a synchrotron beamline; nevertheless this instrument is optimized for resolution, while providing sufficient flux for measuring strongly scattering systems (e.g. nanoparticles). The sample environment is under vacuum, and offers both transmission-mode and grazing-incidence stages. Contact [http://www.bnl.gov/cfn/people/staff.php?q=124 Dmytro Nykypanchuk] or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| [[Cu K-alpha|8.04 keV]]
| 0.005 Å−1 to 0.3 Å−1 (up to ~2 Å−1 using image plate).
| Available through [http://www.bnl.gov/cfn/user/ CFN user program].
|-
|}

==Future Synchrotron Beamlines==
{| class="wikitable"
|-
! Beamline
! Facility
! Status
! Description
! Techniques
! Energy range
! ''q''-range
! Access
|-
| '''[[CMS]]'''
| [[NSLS-II]] at [[BNL]]
| Under construction.
| [[CMS]] is an bending-magnet beamline being constructed at [[NSLS-II]], based in part on the design and hardware at [[X9]] ([[NSLS]]). The beamline will be able to perform transmission and grazing-incidence scattering across a wide ''q''-range (simultaneous SAXS/WAXS possible), and will emphasize automation, high-throughput, and in-situ measurements. Contact [http://staff.ps.bnl.gov/staff.aspx?id=10076 Masa Fukuto], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]]
| 10 keV to 17 keV
| 0.002 Å−1 to 4.2 Å−1
| Will be available through NSLS-II user program.
|-
| '''[[SMI]]'''
| [[NSLS-II]] at [[BNL]]
| Under construction.
| [[SMI]] is a undulator-based beamline being constructed at [[NSLS-II]]. SMI will be a high-flux and high-resolution instrument optimized for grazing-incidence measurements on interfaces, though also capable of performing world-class transmission scattering experiments. [http://staff.ps.bnl.gov/staff.aspx?id=20298 Elaine DiMasi], [http://staff.ps.bnl.gov/staff.aspx?id=83687 Mikhail Zhernenkov], or [http://www.bnl.gov/cfn/people/staff.php?q=150 Kevin Yager] for details.
| [[SAXS]], [[WAXS]], [[GISAXS]], [[GIWAXS]], [[XR]]
| ~2 keV to 24 keV
| Very wide ''q''-range (SAXS and WAXS).
| Will be available through NSLS-II user program.
|-
|}

Cu K-alpha

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'''Copper K-α''' is an [[x-ray]] [[X-ray energy|energy]] frequently used on [[labscale]] x-ray instruments. The energy is 8.04 keV, which corresponds to an x-ray wavelength of 1.5406 Å.

GISAXS measurement time

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The time required for a [[GISAXS]] measurement of course varies based on numerous factors. The most important factors are the flux of the x-ray source, and the inherent scattering power of the sample in question.

Generally, '''a single exposure (2D image) takes on the order of 1 s to 60 s''' at [[synchrotron]] [[beamline]]. The same measurement on a [[labscale]] instrument will of course take considerably longer; typically 10 minutes to a couple hours for a single exposure.

A full measurement on a single sample typically involves [[GISAXS alignment|aligning the sample]] (which will take 2-5 minutes), and then exposures at a variety of incident angles. It is usually a good idea to collect data below the [[critical angle]], near the critical angle, and above the critical angle. This multi-angle data makes eventual data interpretation easier: the sub-critical-angle data provides a measure of the structure in the near-surface region. The data above the critical angle is complementary in that it probes the entire depth of the film. Measurements near the critical angle exhibit strong intensity enhancements, which is useful for weak signals; measurements well above the critical angle yield lower scattering intensity, but the data is less complicated by [[refraction distortion]] and [[dynamic scattering]] (see also [[GTSAXS]]).

In total, '''sample alignment and measurement at 3-8 different incident angles will thus consume approximately 2-10 minutes''' on a synchrotron instrument. Full characterization of a sample may also involve collecting a [[reflectivity]] curve, which will of course increase the measurement time.

==Factors affecting exposure time==
The amount of time required for a single 2D exposure depends on all the same factors that affect the overall [[Tutorial:Qualitative_inspection#Scattering_Intensity|scattering intensity]]. Of course, it is also affected by the desired signal-to-noise ratio (see below).
* '''Beam flux''': Higher flux will decrease the required exposure time. The effect is linear: so doubling the beam flux will half the measurement time. [[Undulator]] beamlines at modern synchrotrons have exceedingly high flux: the required measurement time may only be milliseconds.
* '''Sample volume''': Larger samples of course scatter more. Note that in transmission-mode, if the sample is too thick, it will instead attenuate the scattering (due to [[absorption]] or [[multiple scattering]]). In grazing-incidence experiments, [[GISAXS_sample_requirements#Dimensions|larger sample sizes]] increase scattering power and thus decrease measurement time. However, this is only useful up to a point: if the sample is large enough to fully-capture the incident beam (i.e. there is no spill-over from the [[beam projection]]), then increasing sample dimensions further will not change anything.
* '''Ordering''': More highly ordered systems scatter more strongly.
* '''Scattering contrast''': The higher the electron-density contrast between the structured materials, the strong the signal.

==Signal-to-noise ratio==
The [http://en.wikipedia.org/wiki/Signal-to-noise_ratio signal-to-noise ratio] (SNR) is a measure of data quality, wherein one compares the strength of the signal of interest to the complicating background noise. In x-ray scattering measurements, various kinds of [[background]] (detector background, substrate scattering, instrument windows, air scattering, etc.) worsen the SNR. However, the largest source of noise is frequently simply [http://en.wikipedia.org/wiki/Shot_noise shot noise]: the inherent counting statistics arising from the small number of photons being detected. For integer counting, the SNR goes as:
:<math>
\begin{alignat}{2}
\mathrm{SNR} & = \frac{\mu}{\sigma} \\
& = \sqrt{N}
\end{alignat}
</math>
Where <math>\mu</math> is the (average) signal, and <math>\sigma</math> is the standard deviation of the signal (i.e. the noise), and ''N'' is the integer number of counts. Thus, for a pixel that has 10,000 counts, the SNR is 100.

The above equation makes it clear that improving the SNR is in general difficult: to improve the data quality by a factor of 10, one must increase the measurement time by a factor of 102 = 100. In other words, slightly increasing measurements times does not appreciably improve data quality (one must instead increase measurement times by a meaningful factor).

==Overcounting==
In general, longer exposure times yield better-quality data (higher SNR). However, one must be careful to avoid overcounting.

===Detector saturation===
X-ray detectors can be saturated if the signal is too large. Every detector technology has a limit, with respect to the maximum instantaneous counting rate (which can only be mitigated by attenuating the beam), the maximum pixel count value, and (possibly) a maximum global (whole image) count rate/value.

Fiber-coupled CCD detectors typically have a per-pixel dynamic range of, e.g., 16-bit = 65,536 counts. If a given pixel has more counts than this, the data file will store an erroneous value. The value may be pegged at the max-count, or may instead have a nonsensical value like -1, or the most-significant-bits may be lost, in which case the pixel will have an intermediate (possibly random-seeming) value. This saturation makes data within the saturated pixels useless. Worse still, CCD readout technology introduces cross-talk between pixels (and even between readout modules: i.e. between different regions of the detector image). The end result is that a saturated image may have significant artifacts: the pixels near the saturation region will have erroneous values, entire lines of pixels may become saturated, or 'ghosts' of the saturated data may appear throughout the image.

[[Image:Rect3012.png|thumb|470px|left|Detector image of intense scattering that saturates some pixels near the beam center (during a [[GTSAXS]] measurement). Notice how "ghosts" of the saturated pixels appear in other parts of the image.]]

[[Image:Saturation example02.png|thumb|250px|center|Detector image where an extremely bright reflection saturates pixels (during a [[GIWAXS]] measurement). Notice how, for this detector, the saturated pixels (which are along ''qz'' near the left edge of the detector) cause entire rows of pixels to yield erroneous (zero) values.]]

Some detectors exhibit non-linear response even before saturation occurs. This non-linearity of course makes quantitative interpretation of data impossible. For any given detector, one must take care to avoid collecting data in the saturated or near-saturated (non-linear) regimes. (On the other hand, if all one wants is to get [[Tutorial:Qualitative_inspection|a qualitative sense]] of the sample structure, these artifacts may not matter, as long as one is aware of them.)

Modern hybrid pixel detectors (e.g. the Dectris Pilatus or Eiger technologies) tend to have much larger dynamic range: e.g. they are 20-bit, meaning one only saturates at ~1 million counts within a pixel. This higher dynamic-range is much more forgiving (and these detectors also tend not to exhibit cross-talk between pixels); nevertheless one must again be careful to avoid saturation.

===Sample damage===
Another concern with respect to counting time is sample damage. Synchrotron x-ray beams are extremely bright, and can easily destroy the structure one is attempting to measure. The effect is most pronounced for soft materials (polymers, etc.); and is even more rapid in the presence of oxygen, humidity, or solvent vapours. Performing measurements with the sample in vacuum can help forestall (but not eliminate) sample damage.

One should always be on the lookout for signs of sample damage in the GISAXS data itself. If the same spot is measured repeatedly, and the scattering pattern appears to be changing (in particular becoming broader and 'uglier'), then sample damage may be occurring.

===Mitigation===
The simplest way to mitigate the above effects is to keep the exposure time as short as possible (while still obtaining the data one needs). With respect to measurement time, one can also collect the data in multiple frames. It is quite easy after-the-fact to sum the frames together in order to recover a long-exposure (good SNR) image. On the other hand, one can inspect the images and discard images after sample damage occurs. This multi-exposure is also a simple way to avoid detector saturation: each individual image will not be saturated, and the images can be summed together into a higher bit-depth data file.

Another simple trick to avoid sample damage is to periodically shift the x-ray beam along the (presumably homogeneous) sample. Since the x-ray beam is typically only ~100 microns wide, and most samples are ~5 mm wide, there is ample room to conduct subsequent measurements on 'fresh' spots. Note that substantial sample translation may require [[GISAXS alignment|realignment]] of the sample.

X-ray

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'''X-rays''' are high-energy photons. Thus, they are electromagnetic waves (like radio waves, visible light, ultraviolet light, etc.), but are very high-energy and thus have a small wavelength.

X-rays can be used for [[scattering]] experiments, because their wavelike nature causes [[Fourier transform|interference]] from scattered radiation. Their small wavelength makes them ideal for probing small length-scales (atomic, molecular, and nano), while their high-[[X-ray energy|energy]] allows them to [[Absorption|penetrate]] through samples.

==Production==
X-rays can be generated in [[labscale]] instruments; e.g. using a rotating anode (see [[Cu K-alpha]]). High-flux x-ray beams can be generated using [[synchrotron]]s.

==See Also==
* [[X-ray focusing]]
* [[X-ray energy]]
* [http://en.wikipedia.org/wiki/X-ray Wikipedia: X-ray]

Example:P3HT orientation analysis

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This tutorial describes how to quantify the orientation distribution of the semiconducting polymer [[P3HT]] using [[GIWAXS]]. This orientation analysis is meant to determine the relative amounts of the material oriented in different ways. The same kind of analysis can be applied to other semiconducting polymers or small-molecules. In fact, the same conceptual steps can be applied more broadly to determining any kind of orientation distribution (though one must be careful in interpreting the relationship between [[reciprocal-space]] peaks, which will be different for each material's specific [[unit cell]]).

==P3HT orientation==
P3HT crystallizes into the [[unit cell]] shown below. P3HT crystals are anisotropic, often appearing as long needle-like structures. Note that this unit cell is highly idealized: the alkyl side-chains have considerable freedom and thus disorder (they may even be liquid-like). Moreover, real samples of P3HT organize in a more disordered state than shown here. Although the lamellar stacking is well-defined, and the aromatic (''π''-''π'') stacking is also well-defined, one typically does not observe any scattering peak along the backbone direction: i.e. there is usually no well-defined persistence of order in this direction. It is also likely that subsequent chains do not organize with the well-defined registry shown in the cartoon. Overall, P3HT is thus better thought of as being semi-crystalline or liquid-crystalline: it exhibits considerable molecular order (giving rise to scattering peaks), but is not an extended well-ordered crystal.
[[Image:Cell3-main2.png|thumb|center|300px|Cartoon of an idealized P3HT [[unit cell]].]]
* The lamellar stacking has a spacing of ~1.6 nm, [[Q value|giving rise]] to a peak (100) at ''q'' ~0.4 Å−1.
* The aromatic (''π''-''π'') stacking has a spacing of ~0.39 nm, [[Q value|giving rise]] to a peak (010) at ''q'' ~1.6 Å−1.
* The spacing along the ring direction is too disordered to give a well-defined 001 peak.

When P3HT is cast as a thin-film, this unit cell can adopt a variety of orientations. Although most materials form 3D powders when cast from solution, P3HT adopts a relatively well-defined orientation with respect to the substrate. It seems that the alkyl side-chains preferentially segregate to the film-air and film-substrate interfaces (presumably in order to lower the interfacial energy), which drives the material overall into the ''edge-on'' orientation shown below:

{|
| [[Image:Cell3-edge on2.png|200px|thumb|edge-on]]
| [[Image:Cell3-face on2.png|200px|thumb|face-on]]
| [[Image:Cell3-end on2.png|200px|thumb|end-on]]
|}

Absent any other driving force, the above configurations are assumed to be in-plane isotropic (2D powders). In such a case, one would expect to see [[reciprocal-space]]s corresponding to these states of:

{|
| [[Image:P3ht_rs-edge-on.png|200px|thumb|edge-on]]
| [[Image:P3ht_rs-face-on.png|200px|thumb|face-on]]
| [[Image:P3ht_rs-end-on.png|200px|thumb|end-on]]
| [[Image:P3ht_rs-powder.png|200px|thumb|isotropic]]
|}

Of course, what one observes on the detector is only where the [[Ewald sphere]] intersects [[reciprocal-space]]:

{|
| [[Image:P3ht_det-edge-on.png|200px|thumb|edge-on]]
| [[Image:P3ht_det-face-on.png|200px|thumb|face-on]]
| [[Image:P3ht_det-end-on.png|200px|thumb|end-on]]
| [[Image:P3ht_det-powder.png|200px|thumb|isotropic]]
|}

Summarizing:
* '''Edge-on''' involves the lamellar side-chains wetting the interfaces, which means the lamellar stacking is vertical (100 peak along ''qz''), and the ''π''-''π'' stacking is then in-plane (010 peak along ''qr'').
* '''Face-on''' involves the aromatic rings facing the substrate, which means the lamellar stacking is in-plane (100 peak along ''qr''), and the ''π''-''π'' stacking is in the film normal direction (010 peak along ''qz'').
* '''End-on''' involves the chain ends pointing towards, which means the lamellar stacking is in-plane (100 peak along ''qr''), and the ''π''-''π'' stacking is also in-plane (010 peak along ''qr''). Since the chain axis doesn't give a well-defined peak, there is no scattering along ''qz''.
* '''Isotropic''' involves a complete orientational averaging of the unit cell orientation. The lamellar (100) peak and the ''π''-''π'' (010) peak will both appear to be rings of uniform intensity.

==Example GIWAXS==
Shown below is a typical [[GIWAXS]] image of P3HT cast on a [[Material:Silicon|silicon]] substrate:

[[Image:P3ht-generic giwaxs02.png|450px|center]]

Because of the ''edge-on'' orientation, the lamellar peaks appear along the ''qz'' axis. Below is a comparison of P3HT with different orientation distributions.

{|
| [[Image:P3ht-generic giwaxs.png|300px|center|thumb|[[Material:P3HT|P3HT]] with predominantly '''edge-on''' orientation. The 100 peak is along ''qz'', while the 010 peak is along ''qx''.]]
| [[Image:P3ht-face-on giwaxs.png|300px|center|thumb|P3HT with predominantly '''face-on''' orientation. Notice the 100 peak is along ''qx'', while a weak 010 peak can be seen near the ''qz'' axis.]]
| [[Image:P3ht-isotropic giwaxs.png|300px|center|thumb|P3HT with nearly '''isotropic''' orientation. Notice the extremely broad (nearly uniform) distribution of intensity for all the peaks.]]
|}

==Analysis: In-plane powder==
In order to quantify the orientation distribution of P3HT, we need to measure the intensity of the scattering as a function of angle. We define the azimuthal angle to be ''χ'': this is the angle with respect to the ''qz'' axis. I.e. ''χ'' = 0° is the out-of-plane (''qz'') axis, while ''χ'' = 90° is the in-plane (''qr'') axis.
===Step 1: Conversion to ''q''-space===
The raw detector image needs to be converted into [[reciprocal-space]]. This is typically done by using a [[Materials#Calibration_standards|calibration standard]], which has rings at known ''q''-position. The purpose of calibration is to convert from pixel position to <math>(q_x,q_z)</math> value. One needs to know:
# The [[X-ray energy|x-ray wavelength]]. This is known since it is set by the x-ray source (and/or monochromator).
# The unitless detector distance D/d, where D is the detector distance and d is the detector width. Since d is typically known, one can either measure D directly (even using a tape measure is reasonable accurate), or by noting the pixel position of a ring in calibration standard.
# Direct beam position (i.e. the pixel position of the direct beam). Even with the beam block by a beamstop, low-''q'' beam spillover is usually sufficient to note the beam position. One can also determine the center of scattering rings to define the beam position.
# Detector tilt. This can be assessed by noting the curvature of scattering rings from a standard sample.
With the above information, one can convert from the raw image into data in [[reciprocal-space]] (various pieces of [[software]] will do this for you).

Notice that one can either display the data as <math>(q_x,q_z)</math> or as <math>(q_r,q_z)</math>, where:
:<math>
q_r = \sqrt{ q_x^2 + q_y^2 }
</math>
The <math>(q_x,q_z)</math> representation ignores the ''qy'' component of the [[momentum transfer]]. For small-angle measurements ([[GISAXS]]), this is a reasonable approximation. However for wide-angle ([[GIWAXS]]) measurements, this is a poor approximation: the curvature of the [[Ewald sphere]] means that the part of reciprocal-space probed by the detector is curving away from the <math>(q_x,q_z)</math> plane. As such, in the <math>(q_r,q_z)</math> representation, we note a 'missing wedge' of data near the ''qz'' axis. In fact, in grazing-incidence geometry, we do not probe the ''true'' ''qz'' axis, except at two points (the direct beam position, and the specularly-reflected beam position).

{|
| [[Image:P3ht calibration01.png|thumb|250px|Raw detector image.]]
| [[Image:P3ht calibration02.png|thumb|300px|Data converted to ''q''-space.]]
| [[Image:P3ht calibration03.png|thumb|300px|Data converted to ''q''-space, taking into account Ewald sphere.]]
|}

The conversion to ''q''-space is necessary for all subsequent analysis steps. Moreover, we typically are interested in ''χ'' defined in [[reciprocal-space]] (i.e. with respect to the sample coordinates, not the instrument reference frame), so we should compute ''χ'' in the <math>(q_r,q_z)</math> representation shown above.

===Step 2: Linecut===
From the converted data, we can take a linecut along a ''χ''-arc. In the present analysis, the most useful place to take such a cut is along the 100 lamellar peak (and then along the 010 aromatic stacking peak). When taking the linecut, one should consider:
# When extracting the intensities along the arc, one should try to integrate the full peak width. The integration must be wide enough to take the full peak into account for all ''χ'' (otherwise the intensity will change along ''χ'' simply due to the fraction of the peak one is probing.
# The intensity data should be [[background]]-subtracted. In this case, subtracting the [[Background#Local_background|local background]] makes the most sense: i.e. subtract the intensity just outside the arc of interest. (This must be done at each corresponding ''χ'', since the background may not be isotropic.)
# The ''χ''-scale should be shifted in order to take into account the above-noted curvature of the Ewald sphere. Thus, there will be a small gap in the data near ''χ'' = 0°.
# One should ignore the [[Yoneda]] streak, since it exhibits an intensity enhancement. Any data at ''χ'' beyond the Yoneda should also be discarded since this data comes from below the [[horizon]], and is thus attenuated. For the P3HT 100 peak, this usually means eliminating ''χ'' > ~82°.
# In principle, one should re-adjust the ''χ''-scale to take into account [[refraction distortion]]s: the grazing-incidence geometry induces substantial beam refractions, which causes [[reciprocal-space]] to look warped on the detector image. This distortion only affects the ''qz'' component, and is greatest near the Yoneda. This distortion is substantial in [[GISAXS]], but is usually negligible in [[GIWAXS]].

[[Image:P3ht chi example.png|400px|thumb|center|Example of integrated peak intensity along ''χ''-arcs for an edge-on P3HT sample. The dark line is the lamellar 100 peak, the grey line is the aromatic 010 peak.]]

===Step 3: Account for sample symmetry===
The ''I'' vs. ''χ'' curve shown above can be thought of as the orientation distribution of the P3HT. However, one must be careful in directly interpreting the intensity as representing the ''amount of material''. The reason for this (as usual) is that the [[Ewald sphere]] is probing only a single slice through the 3D reciprocal-space. So we are not probing the full scattering intensity for any given population.

How to properly account for the full scattering intensity depends on sample symmetry. In the most general sense, we can rotate the sample, accumulate multiple images, and reconstruct the full 3D reciprocal-space. However, it is far easier to account for this mathematically, if we know the sample symmetry. It turns out, that for an in-plane powder, we must simply multiply the above curve by <math>\sin(\chi)</math>. For a detailed explanation of why this is the case, refer to [[Integrated intensity|integrated intensity]]. Roughly, this factor arises from the spherical coordinate system, aligned with the symmetry axis of the 2D powder. More heuristically, one can imagine that observed scattering intensity near ''qr'' actually represents a whole ring of scattering in the 3D reciprocal-space. This 'ring' becomes smaller at larger ''χ''; the <math>\sin(\chi)</math> factor exactly accounts for this variation.

{|
| [[Image:p3ht_chi_example02.png|350px]]
| [[Image:p3ht_chi_example03.png|350px]]
|}

The corrected data (right panel above) now has the intensity being proportional to the ''amount of material'' oriented at that ''χ'' angle. This curve can be reported as an orientation distribution for the material (closely related to [[pole figures]]).

===Step 4: Integrate populations===
One can now integrate the intensity in the corrected curve, to come up with estimates of the relative amount of material. There are many ways one could choose to do this. In this example, we divide the scattering intensity into three populations:
* '''Isotropic''': The scattering intensity arising from the subset of grains that form an isotropic distribution.
* '''Edge-on''': The scattering intensity arising from the edge-on grains. We include all grains with an orientation χ<45°.
* '''Face-on''': The scattering intensity arising from the face-on grains. We include all grains with an orientation χ>45°.

Note that we are here assuming that all the intensity from the 100 scattering along ''qr'' arises from entirely from ''face-on'' material. However, both ''face-on'' and ''end-on'' material would give rise to scattering at that position in [[reciprocal-space]]. To differentiate between those two possibilities, one must invoke additional data. Specifically, one can look at the 010 (''π''-''π'') peak: for ''end-on'', the ''π''-''π'' peak will also be in-plane (along ''qr''), whereas for ''face-on'', one should observe substantial intensity of the ''π''-''π'' peak in the out-of-plane direction (near ''qz'' axis).

For the present example, the ''end-on'' orientation was excluded as a possibility, and therefore we ascribe all of the ''qr'' scattering to the ''face-on'' orientation. We compute integrated quantities by summing up the area under the curve, and distributing it into the three categories noted above. Importantly, the isotropic population appears as a uniform baseline (isotropic ring) in the original data, and thus appears as a <math>\sin(\chi)</math> baseline in the corrected data.

{|
| [[Image:Pop schematict03.png|300px|]]
| [[Image:Pop schematict04b.png|300px|]]
|}

Note again that only the intensities in the corrected curve (right panel above) are linearly representative of the ''amount of material''. We can compare the three integrated values to the total, and thereby compute a percentage for edge-on, face-on, and isotropic.

==Analysis: In-plane aligned==
Note that for a sample that ''isn't'' an in-plane powder (e.g. P3HT aligned in a grating), then the above symmetry arguments would change. In that case, one would need to instead account for the orientation distribution in the in-plane direction (''ϕ''). Note that if the material were highly aligned with the grating axis ((''ϕ'' = 0°), then a single measurement in this aligned geometry would be sufficient to assess the full orientation distribution. In other words, the original uncorrected data would correctly represent the relative amounts of material:

[[Image:Pop schematict03.png|300px|]]

See also [[grating alignment]] for caveats related to the in-plane angle (''ϕ'').

==Literature==

===Development/description of analysis method===
* [http://pubs.acs.org/doi/abs/10.1021/nn202515z Nanoimprint-Induced Molecular Orientation in Semiconducting Polymer Nanostructures] Htay Hlaing, Xinhui Lu, Tommy Hofmann, [[Kevin Yager|Kevin G. Yager]], Charles T. Black, and Benjamin M. Ocko ''ACS Nano'' 2011, 5 (9), 7532-7538 [http://dx.doi.org/10.1021/nn202515z doi: 10.1021/nn202515z]
* [http://scitation.aip.org/content/aip/journal/apl/99/16/10.1063/1.3651509 Enhanced charge collection in confined bulk heterojunction organic solar cells] Jonathan E. Allen, [[Kevin G. Yager]], Htay Hlaing, Chang-Yong Nam, Benjamin M. Ocko and Charles T. Black ''Applied Physics Letters'' 2011, 99, 163301. [http://dx.doi.org/10.1063/1.3651509 doi: 10.1063/1.3651509] '''c.f. [ftp://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-99-015142/080111_TemplatedOrganicSolarCells_SupplementaryInformation_APL_final.pdf Supplementary Information]'''
* [http://pubs.acs.org/doi/abs/10.1021/nl301759j One-Volt Operation of High-Current Vertical Channel Polymer Semiconductor Field-Effect Transistors] Johnston, D.E.; [[Kevin Yager|Yager, K.G.]]; Nam, C.-Y.; Ocko, B.M.; Black, C.T. ''Nano Letters'' 2012, 8, 4181–4186 [http://dx.doi.org/10.1021/nl301759j doi: 10.1021/nl301759j]
* '''[http://pubs.acs.org/doi/abs/10.1021/nn4060539 Nanostructured Surfaces Frustrate Polymer Semiconductor Molecular Orientation]''' Johnston, D.E.; [[Kevin Yager|Yager, K.G.]]; Hlaing, H.; Lu, X.; Ocko, B.M.; Black, C.T. ''ACS Nano'' 2014 [http://dx.doi.org/10.1021/nn4060539 doi: 10.1021/nn4060539]

===Application of method===
* [http://pubs.acs.org/doi/abs/10.1021/cm501251n Stable and Controllable Polymer/Fullerene Composite Nanofibers through Cooperative Noncovalent Interactions for Organic Photovoltaics] Fei Li, [[Kevin G. Yager]], Noel M. Dawson, Ying-Bing Jiang, Kevin J. Malloy, and Yang Qin ''Chemistry of Materials'' 2014 [http://dx.doi.org/10.1021/cm501251n doi: 10.1021/cm501251n]
===Related papers===
====Angular correction (curvature of [[Ewald sphere]])====
* '''[http://pubs.acs.org/doi/abs/10.1021/la904840q Quantification of Thin Film Crystallographic Orientation Using X-ray Diffraction with an Area Detector]''' Jessy L. Baker, Leslie H. Jimison, Stefan Mannsfeld, Steven Volkman, Shong Yin, Vivek Subramanian, Alberto Salleo, A. Paul Alivisatos and Michael F. Toney ''Langmuir'' 2010, 26 (11), 9146-9151. [http://dx.doi.org/10.1021/la904840q doi: 10.1021/la904840q]
* [http://scripts.iucr.org/cgi-bin/paper?S0021889808001064 Simulating X-ray diffraction of textured films] D. W. Breiby, O. Bunk, J. W. Andreasen, H. T. Lemke and M. M. Nielsen ''J. Appl. Cryst.'' 2008, 41, 262-271. [http://dx.doi.org/10.1107/S0021889808001064 doi: 10.1107/S0021889808001064]
====sin(angle) correction====
* [http://pubs.acs.org/doi/abs/10.1021/nl501233g Confinement-Driven Increase in Ionomer Thin-Film Modulus] Kirt A. Page, Ahmet Kusoglu, Christopher M. Stafford, Sangcheol Kim, R. Joseph Kline, and Adam Z. Weber ''Nano Letters'' 2014, 14 (5), 2299-2304. [http://dx.doi.org/10.1021/nl501233g doi: 10.1021/nl501233g]
====Other orientation analyses====
* [http://scripts.iucr.org/cgi-bin/paper?S0021889806038957 Evaluation of equatorial orientation distributions] C. Burger and W. Ruland ''J. Appl. Cryst.'' 2006, 39, 889-891. [http://dx.doi.org/10.1107/S0021889806038957 doi: 10.1107/S0021889806038957]
* [http://scripts.iucr.org/cgi-bin/paper?S0021889807010503 Two-dimensional small-angle X-ray scattering of self-assembled nanocomposite films with oriented arrays of spheres: determination of lattice type, preferred orientation, deformation and imperfection] W. Ruland and B. M. Smarsly ''J. Appl. Cryst.'' 2007, 40, 409-417. [http://dx.doi.org/10.1107/S0021889807010503 doi: 10.1107/S0021889807010503]
* [http://pubs.acs.org/doi/abs/10.1021/nl903187v Device-Scale Perpendicular Alignment of Colloidal Nanorods] Jessy L. Baker, Asaph Widmer-Cooper, Michael F. Toney, Phillip L. Geissler and A. Paul Alivisatos ''Nano Letters'' 2010, 10 (1), 195-201. [http://dx.doi.org/10.1021/nl903187v doi: 10.1021/nl903187v]

Example:P3HT orientation analysis

2014-06-20T14:52:07Z

130.199.3.165:

This tutorial describes how to quantify the orientation distribution of the semiconducting polymer [[P3HT]] using [[GIWAXS]]. This orientation analysis is meant to determine the relative amounts of the material oriented in different ways. The same kind of analysis can be applied to other semiconducting polymers or small-molecules. In fact, the same conceptual steps can be applied more broadly to determining any kind of orientation distribution (though one must be careful in interpreting the relationship between [[reciprocal-space]] peaks, which will be different for each material's specific [[unit cell]]).

==P3HT orientation==
P3HT crystallizes into the [[unit cell]] shown below. P3HT crystals are anisotropic, often appearing as long needle-like structures. Note that this unit cell is highly idealized: the alkyl side-chains have considerable freedom and thus disorder (they may even be liquid-like). Moreover, real samples of P3HT organize in a more disordered state than shown here. Although the lamellar stacking is well-defined, and the aromatic (''π''-''π'') stacking is also well-defined, one typically does not observe any scattering peak along the backbone direction: i.e. there is usually no well-defined persistence of order in this direction. It is also likely that subsequent chains do not organize with the well-defined registry shown in the cartoon. Overall, P3HT is thus better thought of as being semi-crystalline or liquid-crystalline: it exhibits considerable molecular order (giving rise to scattering peaks), but is not an extended well-ordered crystal.
[[Image:Cell3-main2.png|thumb|center|300px|Cartoon of an idealized P3HT [[unit cell]].]]
* The lamellar stacking has a spacing of ~1.6 nm, [[Q value|giving rise]] to a peak (100) at ''q'' ~0.4 Å−1.
* The aromatic (''π''-''π'') stacking has a spacing of ~0.39 nm, [[Q value|giving rise]] to a peak (010) at ''q'' ~1.6 Å−1.
* The spacing along the ring direction is too disordered to give a well-defined 001 peak.

When P3HT is cast as a thin-film, this unit cell can adopt a variety of orientations. Although most materials form 3D powders when cast from solution, P3HT adopts a relatively well-defined orientation with respect to the substrate. It seems that the alkyl side-chains preferentially segregate to the film-air and film-substrate interfaces (presumably in order to lower the interfacial energy), which drives the material overall into the ''edge-on'' orientation shown below:

{|
| [[Image:Cell3-edge on2.png|200px|thumb|edge-on]]
| [[Image:Cell3-face on2.png|200px|thumb|face-on]]
| [[Image:Cell3-end on2.png|200px|thumb|end-on]]
|}

Absent any other driving force, the above configurations are assumed to be in-plane isotropic (2D powders). In such a case, one would expect to see [[reciprocal-space]]s corresponding to these states of:

{|
| [[Image:P3ht_rs-edge-on.png|200px|thumb|edge-on]]
| [[Image:P3ht_rs-face-on.png|200px|thumb|face-on]]
| [[Image:P3ht_rs-end-on.png|200px|thumb|end-on]]
| [[Image:P3ht_rs-powder.png|200px|thumb|isotropic]]
|}

Of course, what one observes on the detector is only where the [[Ewald sphere]] intersects [[reciprocal-space]]:

{|
| [[Image:P3ht_det-edge-on.png|200px|thumb|edge-on]]
| [[Image:P3ht_det-face-on.png|200px|thumb|face-on]]
| [[Image:P3ht_det-end-on.png|200px|thumb|end-on]]
| [[Image:P3ht_det-powder.png|200px|thumb|isotropic]]
|}

Summarizing:
* '''Edge-on''' involves the lamellar side-chains wetting the interfaces, which means the lamellar stacking is vertical (100 peak along ''qz''), and the ''π''-''π'' stacking is then in-plane (010 peak along ''qr'').
* '''Face-on''' involves the aromatic rings facing the substrate, which means the lamellar stacking is in-plane (100 peak along ''qr''), and the ''π''-''π'' stacking is in the film normal direction (010 peak along ''qz'').
* '''End-on''' involves the chain ends pointing towards, which means the lamellar stacking is in-plane (100 peak along ''qr''), and the ''π''-''π'' stacking is also in-plane (010 peak along ''qr''). Since the chain axis doesn't give a well-defined peak, there is no scattering along ''qz''.
* '''Isotropic''' involves a complete orientational averaging of the unit cell orientation. The lamellar (100) peak and the ''π''-''π'' (010) peak will both appear to be rings of uniform intensity.

==Example GIWAXS==
Shown below is a typical [[GIWAXS]] image of P3HT cast on a [[Material:Silicon|silicon]] substrate:

[[Image:P3ht-generic giwaxs02.png|450px|center]]

Because of the ''edge-on'' orientation, the lamellar peaks appear along the ''qz'' axis. Below is a comparison of P3HT with different orientation distributions.

{|
| [[Image:P3ht-generic giwaxs.png|300px|center|thumb|[[Material:P3HT|P3HT]] with predominantly '''edge-on''' orientation. The 100 peak is along ''qz'', while the 010 peak is along ''qx''.]]
| [[Image:P3ht-face-on giwaxs.png|300px|center|thumb|P3HT with predominantly '''face-on''' orientation. Notice the 100 peak is along ''qx'', while a weak 010 peak can be seen near the ''qz'' axis.]]
| [[Image:P3ht-isotropic giwaxs.png|300px|center|thumb|P3HT with nearly '''isotropic''' orientation. Notice the extremely broad (nearly uniform) distribution of intensity for all the peaks.]]
|}

==Analysis: In-plane powder==
In order to quantify the orientation distribution of P3HT, we need to measure the intensity of the scattering as a function of angle. We define the azimuthal angle to be ''χ'': this is the angle with respect to the ''qz'' axis. I.e. ''χ'' = 0° is the out-of-plane (''qz'') axis, while ''χ'' = 90° is the in-plane (''qr'') axis.
===Step 1: Conversion to ''q''-space===
The raw detector image needs to be converted into [[reciprocal-space]]. This is typically done by using a [[Materials#Calibration_standards|calibration standard]], which has rings at known ''q''-position. The purpose of calibration is to convert from pixel position to <math>(q_x,q_z)</math> value. One needs to know:
# The [[X-ray energy|x-ray wavelength]]. This is known since it is set by the x-ray source (and/or monochromator).
# The unitless detector distance D/d, where D is the detector distance and d is the detector width. Since d is typically known, one can either measure D directly (even using a tape measure is reasonable accurate), or by noting the pixel position of a ring in calibration standard.
# Direct beam position (i.e. the pixel position of the direct beam). Even with the beam block by a beamstop, low-''q'' beam spillover is usually sufficient to note the beam position. One can also determine the center of scattering rings to define the beam position.
# Detector tilt. This can be assessed by noting the curvature of scattering rings from a standard sample.
With the above information, one can convert from the raw image into data in [[reciprocal-space]] (various pieces of [[software]] will do this for you).

Notice that one can either display the data as <math>(q_x,q_z)</math> or as <math>(q_r,q_z)</math>, where:
:<math>
q_r = \sqrt{ q_x^2 + q_y^2 }
</math>
The <math>(q_x,q_z)</math> representation ignores the ''qy'' component of the [[momentum transfer]]. For small-angle measurements ([[GISAXS]]), this is a reasonable approximation. However for wide-angle ([[GIWAXS]]) measurements, this is a poor approximation: the curvature of the [[Ewald sphere]] means that the part of reciprocal-space probed by the detector is curving away from the <math>(q_x,q_z)</math> plane. As such, in the <math>(q_r,q_z)</math> representation, we note a 'missing wedge' of data near the ''qz'' axis. In fact, in grazing-incidence geometry, we do not probe the ''true'' ''qz'' axis, except at two points (the direct beam position, and the specularly-reflected beam position).

{|
| [[Image:P3ht calibration01.png|thumb|250px|Raw detector image.]]
| [[Image:P3ht calibration02.png|thumb|300px|Data converted to ''q''-space.]]
| [[Image:P3ht calibration03.png|thumb|300px|Data converted to ''q''-space, taking into account Ewald sphere.]]
|}

The conversion to ''q''-space is necessary for all subsequent analysis steps. Moreover, we typically are interested in ''χ'' defined in [[reciprocal-space]] (i.e. with respect to the sample coordinates, not the instrument reference frame), so we should compute ''χ'' in the <math>(q_r,q_z)</math> representation shown above.

===Step 2: Linecut===
From the converted data, we can take a linecut along a ''χ''-arc. In the present analysis, the most useful place to take such a cut is along the 100 lamellar peak (and then along the 010 aromatic stacking peak). When taking the linecut, one should consider:
# When extracting the intensities along the arc, one should try to integrate the full peak width. The integration must be wide enough to take the full peak into account for all ''χ'' (otherwise the intensity will change along ''χ'' simply due to the fraction of the peak one is probing.
# The intensity data should be [[background]]-subtracted. In this case, subtracting the [[Background#Local_background|local background]] makes the most sense: i.e. subtract the intensity just outside the arc of interest. (This must be done at each corresponding ''χ'', since the background may not be isotropic.)
# The ''χ''-scale should be shifted in order to take into account the above-noted curvature of the Ewald sphere. Thus, there will be a small gap in the data near ''χ'' = 0°.
# One should ignore the [[Yoneda]] streak, since it exhibits an intensity enhancement. Any data at ''χ'' beyond the Yoneda should also be discarded since this data comes from below the [[horizon]], and is thus attenuated. For the P3HT 100 peak, this usually means eliminating ''χ'' > ~82°.
# In principle, one should re-adjust the ''χ''-scale to take into account [[refraction distortion]]s: the grazing-incidence geometry induces substantial beam refractions, which distorts [[reciprocal-space]]. This distortion only affects the ''qz'' component, and is greatest near the Yoneda. This distortion is substantial in [[GISAXS]], but is usually negligible in [[GIWAXS]].

[[Image:P3ht chi example.png|400px|thumb|center|Example of integrated peak intensity along ''χ''-arcs for an edge-on P3HT sample. The dark line is the lamellar 100 peak, the grey line is the aromatic 010 peak.]]

===Step 3: Account for sample symmetry===
The ''I'' vs. ''χ'' curve shown above can be thought of as the orientation distribution of the P3HT. However, one must be careful in directly interpreting the intensity as representing the ''amount of material''. The reason for this (as usual) is that the [[Ewald sphere]] is probing only a single slice through the 3D reciprocal-space. So we are not probing the full scattering intensity for any given population.

How to properly account for the full scattering intensity depends on sample symmetry. In the most general sense, we can rotate the sample, accumulate multiple images, and reconstruct the full 3D reciprocal-space. However, it is far easier to account for this mathematically, if we know the sample symmetry. It turns out, that for an in-plane powder, we must simply multiply the above curve by <math>\sin(\chi)</math>. For a detailed explanation of why this is the case, refer to [[Integrated intensity|integrated intensity]]. Roughly, this factor arises from the spherical coordinate system, aligned with the symmetry axis of the 2D powder. More heuristically, one can imagine that observed scattering intensity near ''qr'' actually represents a whole ring of scattering in the 3D reciprocal-space. This 'ring' becomes smaller at larger ''χ''; the <math>\sin(\chi)</math> factor exactly accounts for this variation.

{|
| [[Image:p3ht_chi_example02.png|350px]]
| [[Image:p3ht_chi_example03.png|350px]]
|}

The corrected data (right panel above) now has the intensity being proportional to the ''amount of material'' oriented at that ''χ'' angle. This curve can be reported as an orientation distribution for the material (closely related to [[pole figures]]).

===Step 4: Integrate populations===
One can now integrate the intensity in the corrected curve, to come up with estimates of the relative amount of material. There are many ways one could choose to do this. In this example, we divide the scattering intensity into three populations:
* '''Isotropic''': The scattering intensity arising from the subset of grains that form an isotropic distribution.
* '''Edge-on''': The scattering intensity arising from the edge-on grains. We include all grains with an orientation χ<45°.
* '''Face-on''': The scattering intensity arising from the face-on grains. We include all grains with an orientation χ>45°.

Note that we are here assuming that all the intensity from the 100 scattering along ''qr'' arises from entirely from ''face-on'' material. However, both ''face-on'' and ''end-on'' material would give rise to scattering at that position in [[reciprocal-space]]. To differentiate between those two possibilities, one must invoke additional data. Specifically, one can look at the 010 (''π''-''π'') peak: for ''end-on'', the ''π''-''π'' peak will also be in-plane (along ''qr''), whereas for ''face-on'', one should observe substantial intensity of the ''π''-''π'' peak in the out-of-plane direction (near ''qz'' axis).

For the present example, the ''end-on'' orientation was excluded as a possibility, and therefore we ascribe all of the ''qr'' scattering to the ''face-on'' orientation. We compute integrated quantities by summing up the area under the curve, and distributing it into the three categories noted above. Importantly, the isotropic population appears as a uniform baseline (isotropic ring) in the original data, and thus appears as a <math>\sin(\chi)</math> baseline in the corrected data.

{|
| [[Image:Pop schematict03.png|300px|]]
| [[Image:Pop schematict04b.png|300px|]]
|}

Note again that only the intensities in the corrected curve (right panel above) are linearly representative of the ''amount of material''. We can compare the three integrated values to the total, and thereby compute a percentage for edge-on, face-on, and isotropic.

==Analysis: In-plane aligned==
Note that for a sample that ''isn't'' an in-plane powder (e.g. P3HT aligned in a grating), then the above symmetry arguments would change. In that case, one would need to instead account for the orientation distribution in the in-plane direction (''ϕ''). Note that if the material were highly aligned with the grating axis ((''ϕ'' = 0°), then a single measurement in this aligned geometry would be sufficient to assess the full orientation distribution. In other words, the original uncorrected data would correctly represent the relative amounts of material:

[[Image:Pop schematict03.png|300px|]]

See also [[grating alignment]] for caveats related to the in-plane angle (''ϕ'').

==Literature==

===Development/description of analysis method===
* [http://pubs.acs.org/doi/abs/10.1021/nn202515z Nanoimprint-Induced Molecular Orientation in Semiconducting Polymer Nanostructures] Htay Hlaing, Xinhui Lu, Tommy Hofmann, [[Kevin Yager|Kevin G. Yager]], Charles T. Black, and Benjamin M. Ocko ''ACS Nano'' 2011, 5 (9), 7532-7538 [http://dx.doi.org/10.1021/nn202515z doi: 10.1021/nn202515z]
* [http://scitation.aip.org/content/aip/journal/apl/99/16/10.1063/1.3651509 Enhanced charge collection in confined bulk heterojunction organic solar cells] Jonathan E. Allen, [[Kevin G. Yager]], Htay Hlaing, Chang-Yong Nam, Benjamin M. Ocko and Charles T. Black ''Applied Physics Letters'' 2011, 99, 163301. [http://dx.doi.org/10.1063/1.3651509 doi: 10.1063/1.3651509] '''c.f. [ftp://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-99-015142/080111_TemplatedOrganicSolarCells_SupplementaryInformation_APL_final.pdf Supplementary Information]'''
* [http://pubs.acs.org/doi/abs/10.1021/nl301759j One-Volt Operation of High-Current Vertical Channel Polymer Semiconductor Field-Effect Transistors] Johnston, D.E.; [[Kevin Yager|Yager, K.G.]]; Nam, C.-Y.; Ocko, B.M.; Black, C.T. ''Nano Letters'' 2012, 8, 4181–4186 [http://dx.doi.org/10.1021/nl301759j doi: 10.1021/nl301759j]
* '''[http://pubs.acs.org/doi/abs/10.1021/nn4060539 Nanostructured Surfaces Frustrate Polymer Semiconductor Molecular Orientation]''' Johnston, D.E.; [[Kevin Yager|Yager, K.G.]]; Hlaing, H.; Lu, X.; Ocko, B.M.; Black, C.T. ''ACS Nano'' 2014 [http://dx.doi.org/10.1021/nn4060539 doi: 10.1021/nn4060539]

===Application of method===
* [http://pubs.acs.org/doi/abs/10.1021/cm501251n Stable and Controllable Polymer/Fullerene Composite Nanofibers through Cooperative Noncovalent Interactions for Organic Photovoltaics] Fei Li, [[Kevin G. Yager]], Noel M. Dawson, Ying-Bing Jiang, Kevin J. Malloy, and Yang Qin ''Chemistry of Materials'' 2014 [http://dx.doi.org/10.1021/cm501251n doi: 10.1021/cm501251n]
===Related papers===
====Angular correction (curvature of [[Ewald sphere]])====
* '''[http://pubs.acs.org/doi/abs/10.1021/la904840q Quantification of Thin Film Crystallographic Orientation Using X-ray Diffraction with an Area Detector]''' Jessy L. Baker, Leslie H. Jimison, Stefan Mannsfeld, Steven Volkman, Shong Yin, Vivek Subramanian, Alberto Salleo, A. Paul Alivisatos and Michael F. Toney ''Langmuir'' 2010, 26 (11), 9146-9151. [http://dx.doi.org/10.1021/la904840q doi: 10.1021/la904840q]
* [http://scripts.iucr.org/cgi-bin/paper?S0021889808001064 Simulating X-ray diffraction of textured films] D. W. Breiby, O. Bunk, J. W. Andreasen, H. T. Lemke and M. M. Nielsen ''J. Appl. Cryst.'' 2008, 41, 262-271. [http://dx.doi.org/10.1107/S0021889808001064 doi: 10.1107/S0021889808001064]
====sin(angle) correction====
* [http://pubs.acs.org/doi/abs/10.1021/nl501233g Confinement-Driven Increase in Ionomer Thin-Film Modulus] Kirt A. Page, Ahmet Kusoglu, Christopher M. Stafford, Sangcheol Kim, R. Joseph Kline, and Adam Z. Weber ''Nano Letters'' 2014, 14 (5), 2299-2304. [http://dx.doi.org/10.1021/nl501233g doi: 10.1021/nl501233g]
====Other orientation analyses====
* [http://scripts.iucr.org/cgi-bin/paper?S0021889806038957 Evaluation of equatorial orientation distributions] C. Burger and W. Ruland ''J. Appl. Cryst.'' 2006, 39, 889-891. [http://dx.doi.org/10.1107/S0021889806038957 doi: 10.1107/S0021889806038957]
* [http://scripts.iucr.org/cgi-bin/paper?S0021889807010503 Two-dimensional small-angle X-ray scattering of self-assembled nanocomposite films with oriented arrays of spheres: determination of lattice type, preferred orientation, deformation and imperfection] W. Ruland and B. M. Smarsly ''J. Appl. Cryst.'' 2007, 40, 409-417. [http://dx.doi.org/10.1107/S0021889807010503 doi: 10.1107/S0021889807010503]
* [http://pubs.acs.org/doi/abs/10.1021/nl903187v Device-Scale Perpendicular Alignment of Colloidal Nanorods] Jessy L. Baker, Asaph Widmer-Cooper, Michael F. Toney, Phillip L. Geissler and A. Paul Alivisatos ''Nano Letters'' 2010, 10 (1), 195-201. [http://dx.doi.org/10.1021/nl903187v doi: 10.1021/nl903187v]

Lattice:BCC

2014-06-20T14:50:55Z

130.199.3.165:

'''BCC''' or '''body-centered cubic''' is a cubic [[lattice]] where the symmetry involves an atom/particle sitting in the center of the conceptual [[unit cell]].
==Canonical BCC==
===Symmetry===
* Crystal Family: Cubic
* [http://en.wikipedia.org/wiki/Lattice_system Crystal System]: Cubic
* [http://en.wikipedia.org/wiki/Bravais_lattice#Bravais_lattices_in_3_dimensions Bravais Lattice]: I (bcc)
* Crystal class: Hexoctahedral
* [http://en.wikipedia.org/wiki/Crystallographic_point_group Point Group]: m3m
* Space Group: Im3m
* Particles per unit cell: <math>n=2</math>
* Volume of unit cell: <math>V_d=a^3</math>
* Dimensionality: <math>d=3</math>
* Projected ''d''-dimensional volume: <math>v_d=a^3</math>
* Solid angle: <math>\Omega_d=4\pi</math>
* Nearest-neighbor distance: <math>d_{nn}=\sqrt{3}a/2</math>
* Assuming spherical particles of radius ''R'':
** Particle volume fraction: <math>\phi=8 \pi R^3/\left(3a^3\right)</math>
** Maximum volume fraction: <math>\phi_{max}=\pi\sqrt{3}/8\approx0.680</math> when <math>R=a\sqrt{3}/4</math>

===Structure===
Body-centered cubic (BCC) is a cubic lattice where a cube-shaped unit cell has particles at each corner of the cube, plus a particle in the center of this cube. The minimal unit cell has only two particles.

[[Image:Bcc01.png|300px]] [[Image:Bcc02-unit cell.png|300px]]

The extended lattice can be thought of in terms of two inter-penetrating [[Lattice:SC|simple cubic]] lattices:

[[Image:Bcc03-lattice.png|400px|left]] [[Image:Bcc04-two lattices.png|400px]]

One can also consider the BCC to be a [[FCC_to_BCC|distorted FCC]]:

[[Image:Fcc to bcc075.png|400px]]

===Neighbors===
Each particle is equivalent (there is nothing special about the 'center' particle in a homogeneous BCC). For a lattice of edge-length ''a'', each particle has 8 "diagonal" nearest-neighbors at a distance of:
::<math>d_{\mathrm{nn}} = \sqrt{3}/2 \times a \approx 0.866 a</math>
and another 6 "direct" next-nearest-neighbors at a distance of <math>a=(2/ \sqrt{3}) d_{nn}</math>.

[[Image:Bcc05-mini cell.png|300px]] [[Image:Bcc05-mini cell2.png|300px]] [[Image:Bcc05-mini cell3.png|300px]]

===[[Reciprocal-space]] Peaks===
* Allowed reflections:
*: <math>f_{hkl} = 2 \,\,\, \mathrm{for} \,\,\, h+k+l=\mathrm{even}</math>
* Peak multiplicities:
*:: <math>m_{h00}=6</math>
*:: <math>m_{hh0}=12</math>
*:: <math>m_{hhh}=8</math>
*:: <math>m_{hk0}=24</math>
*:: <math>m_{hhk}=24</math>
*:: <math>m_{hkl}=48</math>
* Peak positions:
*: <math>q_{hkl}=\frac{2\pi}{a}\sqrt{h^2+k^2+l^2}</math>
*: For ''a'' = 1.0:
<pre>
peak q value h,k,l m f intensity
1: 8.885765876317 1,1,0 12 2 48
2: 12.566370614359 2,0,0 6 2 24
3: 15.390597961942 2,1,1 24 2 96
4: 17.771531752633 2,2,0 12 2 48
5: 19.869176531592 3,1,0 24 2 96
6: 21.765592370811 2,2,2 8 2 32
7: 23.509526717078 3,2,1 48 2 192
8: 25.132741228718 4,0,0 6 2 24
9: 26.657297628950 4,1,1 36 2 144
10: 28.099258924163 4,2,0 24 2 96
11: 29.470751386686 3,3,2 24 2 96
12: 30.781195923885 4,2,2 24 2 96
13: 32.038084488828 5,1,0 72 2 288
14: 34.414423257273 5,2,1 48 2 192
15: 35.543063505267 4,4,0 12 2 48
16: 36.636951272563 5,3,0 48 2 192
17: 37.699111843078 6,0,0 30 2 120
18: 38.732155490827 6,1,1 72 2 288
19: 39.738353063184 6,2,0 24 2 96
20: 40.719694735877 5,4,1 48 2 192
21: 41.677936304377 6,2,2 24 2 96
22: 42.614636098416 6,3,1 48 2 192
23: 43.531184741621 4,4,4 8 2 32
24: 44.428829381584 5,5,0 60 2 240
25: 45.308693596556 6,4,0 24 2 96
26: 46.171793885827 6,3,3 48 2 192
27: 47.019053434156 6,4,2 48 2 192
28: 49.473850582607 6,5,1 48 2 192
29: 51.044838738971 5,5,4 24 2 96
30: 51.812473373661 6,4,4 24 2 96
31: 52.568899858234 6,5,3 48 2 192
32: 53.314595257900 6,6,0 12 2 48
33: 54.775539595071 6,6,2 24 2 96
34: 58.267863475287 6,5,5 24 2 96
35: 58.941502773372 6,6,4 24 2 96
36: 65.296777112432 6,6,6 8 2 32
</pre>
[[Image:Lattice_peaks-BCC.png|450px]]

===Examples===
====Elemental====
: 3. [http://en.wikipedia.org/wiki/Lithium Lithium (Li)] (''a'' = 3.509 Å)
: 11. [http://en.wikipedia.org/wiki/Sodium Sodium (Na)] (''a'' = 4.291 Å)
: 19. [http://en.wikipedia.org/wiki/Potassium Potassium( K)] (''a'' = 5.247 Å) (at 78 K)
: 23. [http://en.wikipedia.org/wiki/Vanadium Vanadium (V)] (''a'' = 3.024 Å)
: 24. [http://en.wikipedia.org/wiki/Chromium Chromium (Cr)] (''a'' = 2.884 Å)
: 26. [http://en.wikipedia.org/wiki/Iron Iron (Fe)] (''a'' = 2.866 Å)
: 37. [http://en.wikipedia.org/wiki/Rubidium Rubidium (Rb)] (''a'' = 5.605 Å) (at 78 K)
: 41. [http://en.wikipedia.org/wiki/Niobium Niobium (Nb)] (''a'' = 3.300 Å)
: 42. [http://en.wikipedia.org/wiki/Molybdenum Molybdenum (Mo)] (''a'' = 3.147 Å)
: 55. [http://en.wikipedia.org/wiki/Caesium Caesium (Cs)] (''a'' = 6.067 Å) (at 78 K)
: 56. [http://en.wikipedia.org/wiki/Barium Barium (Ba)] (''a'' = 5.025 Å)
: 63. [http://en.wikipedia.org/wiki/Europium Europium (Eu)] (''a'' = 4.606 Å)
: 73. [http://en.wikipedia.org/wiki/Tantalum Tantalum (Ta)] (''a'' = 3.306 Å)
: 74. [http://en.wikipedia.org/wiki/Tungsten Tungsten (W)] (''a'' = 3.165 Å)

====Atomic====
* TBD
====Nano====
* TBD

==Body-centered Two-particle==
A lattice where the unit cell has two distinct atoms/particles, arranged with one at the center of the simple cubic lattice defined by the other, has [[Lattice:Simple Cubic|simple cubic]] symmetry. This lattice is often called '''CsCl'''.

[[Image:Bcc-two particle.png|300px]]

===Symmetry===
* Crystal Family: Cubic
* [http://en.wikipedia.org/wiki/Lattice_system Crystal System]: Cubic
* [http://en.wikipedia.org/wiki/Bravais_lattice#Bravais_lattices_in_3_dimensions Bravais Lattice]: P (pcc)
* Crystal class: Hexoctahedral
* [http://en.wikipedia.org/wiki/Crystallographic_point_group Point Group]: m3m
* Space Group: Pm3m
* Particles per unit cell: <math>n=2</math> (distinct)
* Volume of unit cell: <math>V_d=a^3</math>
* Dimensionality: <math>d=3</math>
* Projected ''d''-dimensional volume: <math>v_d=a^3</math>
* Solid angle: <math>\Omega_d=4\pi</math>
* Nearest-neighbor distance: <math>d_{nn}=\sqrt{3}a/2</math>

===Examples===
====Atomics====
* [http://en.wikipedia.org/wiki/Cesium_chloride Cesium chloride (CsCl)] (''a'' = 4.11 Å)

==Body-centered with Edges and Faces==
The BCC lattice, where a second particle type occupies positions along edges and faces. The symmetry is the same as the canonical BCC. (The particles at the face position are effective 'edge' particles with respect to the center particle...)

[[Image:Bcc-faces and edges.png|400px]]

===Particle Positions===
There are 27 positions, with 8 particles in the unit cell
====Particle A====
These are the usual BCC positions. There are 9 positions. In total there are 2 particles in the unit cell:
* <math> 8 \, \mathrm{corners} \, \times \, \frac{1}{8} = 1</math>
** <math>\left(0,0,0\right),(0,0,1),(0,1,0),(1,0,0),(0,1,1),(1,0,1),(1,1,0),(1,1,1)</math>
* <math> 1 \, \mathrm{center} \, \times \, 1 = 1</math>
** <math>\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)</math>

====Particle B====
There are 18 positions, with 6 particles in the unit cell.
* <math> 6 \, \mathrm{faces} \, \times \, \frac{1}{2} = 3</math>
** <math>\left(0,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},0,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},0\right),\left(1,\frac{1}{2},\frac{1}{2}\right),\left(\frac{1}{2},1,\frac{1}{2}\right),\left(\frac{1}{2},\frac{1}{2},1\right)</math>
* <math> 12 \, \mathrm{edges} \, \times \, \frac{1}{4} = 3</math>
** <math>\left(\frac{1}{2},0,0\right) , \left(0,\frac{1}{2},0\right) , \left(0,0,\frac{1}{2}\right) </math>
** <math>\left(1,0,\frac{1}{2}\right) , \left(1,1,\frac{1}{2}\right) , \left(0,1,\frac{1}{2}\right) , \left(\frac{1}{2},1,0\right) , \left(1,\frac{1}{2},0\right) , \left(\frac{1}{2},0,1\right) , \left(0,\frac{1}{2},1\right), \left(1,\frac{1}{2},1\right) , \left(\frac{1}{2},1,1\right) </math>

==See Also==
* [http://en.wikipedia.org/wiki/Cubic_crystal_system Wikipedia: Cubic crystal system]

X-ray

2014-06-20T14:48:26Z

130.199.3.165:

'''X-rays''' are high-energy photons. Thus, they are electromagnetic waves (like radio waves, visible light, ultraviolet light, etc.), but are very high-energy and thus have a small wavelength.

X-rays can be used for [[scattering]] experiments, because their wavelike nature causes [[Fourier transform|interference]] from scattered radiation. Their small wavelength makes them ideal for probing small length-scales (atomic, molecular, and nano), while their high-[[X-ray energy|energy]] allows them to [[Absorption|penetrate]] through samples.

==Production==
X-rays can be generated in labscale instruments; e.g. using a rotating anode (see [[Cu K-alpha]]). High-flux x-ray beams can be generated using [[synchrotron]]s.

==See Also==
* [[X-ray focusing]]
* [[X-ray energy]]
* [http://en.wikipedia.org/wiki/X-ray Wikipedia: X-ray]

Scattering

2014-06-20T14:46:41Z

130.199.3.165:

'''Scattering''' broadly refers to experimental techniques that use the interaction between radiation and matter to elucidate structure. In [[x-ray]] scattering, a collimated x-ray beam is directed at a sample of interest. The incident x-rays scatter off of all the atoms/particles in the sample. Because of the wavelike nature of x-rays (which are simply high-energy photons; i.e. electromagnetic rays), the scattered waves interfere with one another, leading to constructive interference at some angles, but destructive interference at other angles. The final end result is a pattern of scattered radiation (as a function of angle with respect to the direct beam) that encodes the microscopic, nanoscopic, and molecular-scale structure of the sample.

==Geometry==
We define a vector in [[reciprocal-space]] as the difference between the incident and scattered x-ray beams. This new vector is the [[momentum transfer]], denoted by '''q''':
:<math>
\begin{alignat}{2}
\mathbf{q} & = \mathbf{k}_o - \mathbf{k}_i \\
& = k(\mathbf{s}_o - \mathbf{s}_i) \\
& = \frac{2 \pi}{\lambda}(\mathbf{s}_o - \mathbf{s}_i)
\end{alignat}
</math>

The length of this vector is:
:<math>
\begin{alignat}{2}
q = |\mathbf{q}| & = k \sin { \theta } \\
& = \frac{2 \pi}{\lambda} \sin{ \theta } \\
& = \frac{4 \pi}{\lambda} \sin{ \theta /2}
\end{alignat}
</math>

==Theory==
The mathematical form of scattering is closely related to the [[Fourier transform]]. The sample's realspace density distribution is Fourier transformed into an abstract 3D [[reciprocal-space]]; scattering probes this inverse space.

Scattering

2014-06-20T14:46:10Z

130.199.3.165:

'''Scattering''' broadly refers to experimental techniques that use the interaction between radiation and matter to elucidate structure. In x-ray scattering, a collimated x-ray beam is directed at a sample of interest. The incident x-rays scatter off of all the atoms/particles in the sample. Because of the wavelike nature of x-rays (which are simply high-energy photons; i.e. electromagnetic rays), the scattered waves interfere with one another, leading to constructive interference at some angles, but destructive interference at other angles. The final end result is a pattern of scattered radiation (as a function of angle with respect to the direct beam) that encodes the microscopic, nanoscopic, and molecular-scale structure of the sample.

==Geometry==
We define a vector in [[reciprocal-space]] as the difference between the incident and scattered x-ray beams. This new vector is the [[momentum transfer]], denoted by '''q''':
:<math>
\begin{alignat}{2}
\mathbf{q} & = \mathbf{k}_o - \mathbf{k}_i \\
& = k(\mathbf{s}_o - \mathbf{s}_i) \\
& = \frac{2 \pi}{\lambda}(\mathbf{s}_o - \mathbf{s}_i)
\end{alignat}
</math>

The length of this vector is:
:<math>
\begin{alignat}{2}
q = |\mathbf{q}| & = k \sin { \theta } \\
& = \frac{2 \pi}{\lambda} \sin{ \theta } \\
& = \frac{4 \pi}{\lambda} \sin{ \theta /2}
\end{alignat}
</math>

==Theory==
The mathematical form of scattering is closely related to the [[Fourier transform]]. The sample's realspace density distribution is Fourier transformed into an abstract 3D [[reciprocal-space]]; scattering probes this inverse space.

X-ray

2014-06-20T14:44:21Z

130.199.3.165:

'''X-rays''' are high-energy photons. They can be used for [[scattering]] experiments, because their wavelike nature causes interference from scattered radiation. Their small wavelength makes them ideal for probing small length-scales (atomic, molecular, and nano), while their high-[[X-ray energy|energy]] allows them to [[Absorption|penetrate]] through samples.

==Production==
X-rays can be generated in labscale instruments; e.g. using a rotating anode (see [[Cu K-alpha]]). High-flux x-ray beams can be generated using [[synchrotron]]s.

==See Also==
* [[X-ray focusing]]
* [[X-ray energy]]
* [http://en.wikipedia.org/wiki/X-ray Wikipedia: X-ray]

X-ray

2014-06-20T14:43:56Z

130.199.3.165: /* See Also */

'''X-rays''' are high-energy photons. They can be used for [[scattering]] experiments, because their wavelike nature causes interference from scattered radiation. Their small wavelength makes them ideal for probing small length-scales (atomic, molecular, and nano), while their high-[[X-ray energy|energy]] allows them to penetrate through samples.

==Production==
X-rays can be generated in labscale instruments; e.g. using a rotating anode (see [[Cu K-alpha]]). High-flux x-ray beams can be generated using [[synchrotron]]s.

==See Also==
* [[X-ray focusing]]
* [[X-ray energy]]
* [http://en.wikipedia.org/wiki/X-ray Wikipedia: X-ray]

Cu K-alpha

2014-06-20T14:43:01Z

130.199.3.165:

'''Copper K-α''' is an [[x-ray]] [[X-ray energy|energy]] frequently used on labscale x-ray instruments. The energy is 8.04 keV, which corresponds to an x-ray wavelength of 1.5406 Å.

X-ray

2014-06-20T14:42:19Z

130.199.3.165: /* Production */

'''X-rays''' are high-energy photons. They can be used for [[scattering]] experiments, because their wavelike nature causes interference from scattered radiation. Their small wavelength makes them ideal for probing small length-scales (atomic, molecular, and nano), while their high-[[X-ray energy|energy]] allows them to penetrate through samples.

==Production==
X-rays can be generated in labscale instruments; e.g. using a rotating anode (see [[Cu K-alpha]]). High-flux x-ray beams can be generated using [[synchrotron]]s.

==See Also==
* [[X-ray focusing]]
* [[X-ray energy]]

X-ray

2014-06-20T14:41:57Z

130.199.3.165: Created page with "'''X-rays''' are high-energy photons. They can be used for scattering experiments, because their wavelike nature causes interference from scattered radiation. Their small ..."

'''X-rays''' are high-energy photons. They can be used for [[scattering]] experiments, because their wavelike nature causes interference from scattered radiation. Their small wavelength makes them ideal for probing small length-scales (atomic, molecular, and nano), while their high-[[X-ray energy|energy]] allows them to penetrate through samples.

==Production==
X-rays can be generated in labscale instruments; e.g. using a rotating anode (see [[Copper K-alpha]]). High-flux x-ray beams can be generated using [[synchrotron]]s.

==See Also==
* [[X-ray focusing]]
* [[X-ray energy]]

X-rays

2014-06-20T14:37:33Z

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#REDIRECT [[X-Ray]

Atomic scattering factors

2014-06-05T20:40:13Z

130.199.3.165: /* Elemental dependence */

The '''atomic scattering factors''' are measures of the [[scattering]] power of individual atoms. Each element has a different atomic scattering factor, which represents how strongly x-rays interact with those atoms.

The scattering factor has two components: ''f''1 and ''f''2, which describe the dispersive and absorptive components. In other words, ''f''2 describes how strongly the material absorbs the radiation, while ''f''1 describes the non-absorptive interaction (which leads to [[Refractive_index|refraction]]).

==Elemental dependence==
Because x-ray interactions occur with an atom's electron cloud, the scattering factors increase with number of electrons, and thus with atomic number (''Z''). However, the relationship between ''f'' and ''Z'' is not monotonic, owing to resonant ([[absorption ]]) edges.

==Energy dependence==
The atomic scattering factors vary with x-ray wavelength. In particular, a given element will have resonant edges at certain energies, where the absorption increases markedly. The dispersive component ''f''1 will also vary rapidly in the vicinity of an absorption edge (c.f. [http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations Kramers-Kronig relations]).

===Examples===

====[[Material:Silicon|silicon]]====

[[Image:Silicon-atomic scatt factor.png|400px|[[Atomic scattering factors]] (''f''1 and ''f''2).]]

====[[Material:Gold|gold]]====

[[Image:Gold-atomic scatt factor.png|400px|[[Atomic scattering factors]] (''f''1 and ''f''2).]]

==See Also==
* [http://henke.lbl.gov/optical_constants/asf.html Periodic table of atomic scattering factors]: Useful tool for looking up the values for any element.
* [http://reference.iucr.org/dictionary/Atomic_scattering_factor Online Dictionary of Crystallography: Atomic scattering factor]

Atomic scattering factors

2014-06-05T20:38:12Z

130.199.3.165:

The '''atomic scattering factors''' are measures of the [[scattering]] power of individual atoms. Each element has a different atomic scattering factor, which represents how strongly x-rays interact with those atoms.

The scattering factor has two components: ''f''1 and ''f''2, which describe the dispersive and absorptive components. In other words, ''f''2 describes how strongly the material absorbs the radiation, while ''f''1 describes the non-absorptive interaction (which leads to [[Refractive_index|refraction]]).

==Elemental dependence==
Because x-ray interactions occur with an atom's electron cloud, the scattering factors increase with number of electrons, and thus with atomic number (''Z''). However, resonant ([[absorption ]]) edges change the scattering factors.

==Energy dependence==
The atomic scattering factors vary with x-ray wavelength. In particular, a given element will have resonant edges at certain energies, where the absorption increases markedly. The dispersive component ''f''1 will also vary rapidly in the vicinity of an absorption edge (c.f. [http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations Kramers-Kronig relations]).

===Examples===

====[[Material:Silicon|silicon]]====

[[Image:Silicon-atomic scatt factor.png|400px|[[Atomic scattering factors]] (''f''1 and ''f''2).]]

====[[Material:Gold|gold]]====

[[Image:Gold-atomic scatt factor.png|400px|[[Atomic scattering factors]] (''f''1 and ''f''2).]]

==See Also==
* [http://henke.lbl.gov/optical_constants/asf.html Periodic table of atomic scattering factors]: Useful tool for looking up the values for any element.
* [http://reference.iucr.org/dictionary/Atomic_scattering_factor Online Dictionary of Crystallography: Atomic scattering factor]

Atomic scattering factors

2014-06-05T15:48:47Z

130.199.3.165: /* Energy dependence */

The '''atomic scattering factors''' are measures of the [[scattering]] power of individual atoms. Each element has a different atomic scattering factor (which in turn varies with x-ray energy), which represents how strongly x-rays interact with those atoms. Because x-ray interactions occur with an atom's electron cloud, the scattering factors increase with number of electrons, and thus with atomic number (''Z'').

The scattering factor has two components: ''f''1 and ''f''2, which describe the dispersive and absorptive components. In other words, ''f''2 describes how strongly the material absorbs the radiation, while ''f''1 describes the non-absorptive interaction (which leads to [[Refractive_index|refraction]]).

==Energy dependence==
The atomic scattering factors vary with x-ray wavelength. In particular, a given element will have resonant edges at certain energies, where the absorption increases markedly. The dispersive component ''f''1 will also vary rapidly in the vicinity of an absorption edge (c.f. [http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations Kramers-Kronig relations]).

===Examples===

====[[Material:Silicon|silicon]]====

[[Image:Silicon-atomic scatt factor.png|400px|[[Atomic scattering factors]] (''f''1 and ''f''2).]]

====[[Material:Gold|gold]]====

[[Image:Gold-atomic scatt factor.png|400px|[[Atomic scattering factors]] (''f''1 and ''f''2).]]

==See Also==
* [http://henke.lbl.gov/optical_constants/asf.html Periodic table of atomic scattering factors]: Useful tool for looking up the values for any element.
* [http://reference.iucr.org/dictionary/Atomic_scattering_factor Online Dictionary of Crystallography: Atomic scattering factor]

Scattering Length Density

2014-06-05T13:06:32Z

130.199.3.165: /* Calculating */

The '''Scattering Length Density''' ('''SLD''', sometimes denoted ''Nb'') is a measure of the scattering power of a material. It increases with the physical density (how tightly packed the scattering entities are), as well as the intrinsic scattering power of the 'scattering entities'. For x-rays, the scattering arises from the electron density, whereas for neutrons, the scattering arises from the nuclear scattering lengths.

==Calculating==
SLD can be computed from the scattering lengths and material densities. Specifically:
:<math>\mathrm{SLD} = \frac{\sum_{i=1}^{N}b_i}{V_m}</math>
where we sum the scattering length contributions (''bi'') from the ''N'' atoms within the [[unit cell]], and divide by the volume, ''Vm'' of this 'unit cell'. Note that the 'unit cell' need not be a crystallographic unit cell: it is simply a representative volume of the material in question: the atoms within it may be arranged randomly (e.g. amorphous material) or in a crystalline way. For instance for a single molecule, ''Vm'' is simply the molecular volume, and the sum includes all the atoms in the molecule. In general we don't know what the appropriate 'molecular volume' should be, but we can compute it from the known bulk density of the material (<math>\rho</math>) and the molecular weight (''MW''):
::<math>V_m = \frac{ \mathrm{MW} }{\rho N_a}</math>
Where ''Na'' is the Avogadro constant. Thus:
:<math>\mathrm{SLD} = \frac{\sum_{i=1}^{N}b_i}{V_m} = \frac{\rho N_a \sum_{i=1}^{N}b_i}{\sum_{i=1}^{N}\mathrm{M}_i} </math>
where M''i'' is the atomic molar mass for each element. Note that the above sum is over ''every atom'' in the representative volume (i.e. a particular atom repeated twice should be added twice). The equation can be recast in terms of weighting factors (stoichiometric numbers in a chemical formula, or concentrations in a mixture) to yield:
:<math>\mathrm{SLD} = \frac{\rho N_a \sum_{i=1}^{N} c_i b_i}{\sum_{i=1}^{N} c_i \mathrm{M}_i} </math>

===Neutron scattering lengths===
For neutrons, the ''bi'' in the above equation are the neutron scattering lengths for the atoms in question. This value depends on the strength of the interaction between a neutron and a given nucleus. It is in general not easy to predict this quantity theoretically; instead experiments are performed to tabulate the scattering lengths. Refer to the [http://www.ill.eu/quick-links/publications/ neutron data booklet] (starting on page 1.1-8) for tables of ''bi'' for known isotopes.

===X-ray scattering lengths===
For x-rays, the scattering arises from the interaction between the incident wave and the electron clouds of the atoms in the material. Thus, the scattering power scales with electron density in the material (with corrections for additional effects, such as [[resonant scattering]], a.k.a. absorption lines). In practice, one can look up tabulated values of the [[atomic scattering factor]] for the atom in question. From this, one can compute the scattering length using:
:<math>
\begin{alignat}{2}
b_i & = \frac{ e^2 }{ 4 \pi \varepsilon_0 m_e c^2}f_1 \\
& = r_e f_1
\end{alignat}
</math>
Where ''f''1 is the real part of the atomic scattering factor, ''e'' is the [http://en.wikipedia.org/wiki/Elementary_charge charge of the electron] (1.602176565×10−19 coulombs), ''ε''0 is the [http://en.wikipedia.org/wiki/Vacuum_permittivity permittivity of free space] (8.854187817x10−12 F/m), ''me'' is the [http://en.wikipedia.org/wiki/Electron_rest_mass mass of the electron] (9.10938215×10−31 kg), and ''c'' is the [http://en.wikipedia.org/wiki/Speed_of_light speed of light] (299,792,458 m/s).

The prefactor to ''f''1 is simply the [http://en.wikipedia.org/wiki/Classical_electron_radius classical electron radius] (''re''), and has the value 2.8179403x10−15 m.

==Converting==
SLD is typically used in the neutron scattering community, but is less common in x-ray scattering. The SLD can be converted to the x-ray [[refractive index]] using:
:<math>
\delta = \frac{\lambda^2}{2 \pi} \mathrm{Re}(\mathrm{SLD})
</math>
:<math>
\beta = \frac{\lambda^2}{2 \pi} \mathrm{Im}(\mathrm{SLD})
</math>

==See Also==
* [[Critical angle]]
* [http://www.ncnr.nist.gov/resources/activation/ SLD calculator]: NIST Center for Neutron Research calculator for predicting SLD.

Critical angle

2014-06-05T13:03:35Z

130.199.3.165: /* From refractive index */

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.

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.

==Examples==
{| class="wikitable"
|-
! Material
! density (g/cm3)
! X-ray energy (keV)
! X-ray wavelength (Å)
! critical angle (°)
! ''qc'' (Å−1)
! SLD (10−6Å−2)
|-
| [[Material:Silicon|Si]]
| 2.3290
| 2.0
| 6.20
| 0.824
| 0.0291
| 16.89
|-
|
|
| 4.0
| 3.10
| 0.451
| 0.0319
| 20.28
|-
|
|
| 8.0
| 1.55
| 0.224
| 0.0317
| 20.07
|-
|
|
| 12.0
| 1.03
| 0.149
| 0.0317
| 19.92
|-

|
|
| 16.0
| 0.77
| 0.112
| 0.0316
| 19.84
|-
|
|
| 24.0
| 0.52
| 0.07426
| 0.0315
| 19.77
|-
|}

{| class="wikitable"
|-
! Material
! density (g/cm3)
! X-ray energy (keV)
! X-ray wavelength (Å)
! critical angle (°)
! ''qc'' (Å−1)
! SLD (10−6Å−2)
|-
| [[Material:Silicon dioxide|SiO2]]
| 2.648
| 2.0
| 6.20
| 0.927
| 0.0328
| 21.42
|-
|
|
| 4.0
| 3.10
| 0.480
| 0.0340
| 22.96
|-
|
|
| 8.0
| 1.55
| 0.239
| 0.0338
| 22.71
|-
|
|
| 12.0
| 1.03
| 0.159
| 0.0337
| 22.58
|-
|
|
| 16.0
| 0.77
| 0.119
| 0.0337
| 22.53
|-
|
|
| 24.0
| 0.52
| 0.079
| 0.0336
| 22.48
|}

{| class="wikitable"
|-
! Material
! density (g/cm3)
! X-ray energy (keV)
! X-ray wavelength (Å)
! critical angle (°)
! ''qc'' (Å−1)
! SLD (10−6Å−2)
|-
| [[Material:Gold|Au]]
| 19.32
| 2.0
| 6.20
| 1.830
| 0.0647
| 83.44
|-
|
|
| 4.0
| 3.10
| 1.097
| 0.0776
| 119.89
|-
|
|
| 8.0
| 1.55
| 0.560
| 0.0792
| 124.86
|-
|
|
| 12.0
| 1.03
| 0.348
| 0.0738
| 108.29
|-
|
|
| 16.0
| 0.77
| 0.282
| 0.0797
| 126.51
|-
|
|
| 24.0
| 0.52
| 0.191
| 0.0811
| 130.80
|}

==Calculating==
The critical angle for a material can be calculated in a variety of ways. For an elemental substance, [http://henke.lbl.gov/optical_constants/pert_form.html this online tool] will calculate it for you.
===From SLD===
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:
::<math> \begin{alignat}{2}
\mathbf{q} & = \mathbf{k}_o-\mathbf{k}_i \\
|\mathbf{q}| & = q = 2 |k| \sin\theta_i = \frac{4 \pi}{\lambda}\sin\theta_i
\end{alignat}
</math>
Where ''λ'' is the wavelength of the x-rays. So:
:<math>
\begin{alignat}{2}
\theta_c & = \arcsin\left( \frac{ q_c \lambda }{4 \pi} \right) \\
& = \arcsin\left( \frac{ \lambda \sqrt{16 \pi \mathrm{SLD} } }{4 \pi} \right) \\
& \approx \sqrt{\frac{\lambda^2 \mathrm{SLD} }{\pi}}
\end{alignat}
</math>

===From refractive index===
The critical angle is simply a result of the refractive index contrast between the film and the ambient. Of course, in this case we are talking about the '''x-ray [[refractive index]]''' (not the usual refractive index for visible light). In the case of neutrons, the film similarly exhibits a neutron refractive index. The refractive index is complex:
:<math>
n = 1 - \delta + i \beta
</math>
For x-rays, the values of ''𝛿'' and ''β'' can be calculated from the [[atomic scattering factors]] (''f''1 and ''f''2) using:
:<math>
\delta = \frac{ n_a r_e \lambda^2 }{2 \pi} f_1
</math>
:<math>
\beta = \frac{ n_a r_e \lambda^2 }{2 \pi} f_2
</math>
Where ''re'' is the [http://en.wikipedia.org/wiki/Classical_electron_radius classical electron radius] (2.8179403x10−15 m), ''λ'' is the wavelength of the probing x-rays, and ''na'' is the number density:
:<math>
n_a = \frac{\rho N_a}{M_a}
</math>
where ''ρ'' is the physical density (e.g. in g/cm3), ''Na'' is the [http://en.wikipedia.org/wiki/Avogadro_constant Avogadro constant] (6.02214129x1023 mol−1), and ''Ma'' is molar mass (e.g. in g/mol). There are also [http://henke.lbl.gov/optical_constants/getdb2.html online tools] that will compute the refractive index for you.

Once the real part of the refractive index (''𝛿'') is known, conversion to critical angle is straightforward:
:<math>
\theta_c = \sqrt{ 2 \delta }
</math>
Note that the resultant critical angle has units of ''radians''. For a multi-component system, one simply uses a weighted sum of the contributions from each element:
:<math>
\theta_c = \sqrt{ \frac{\rho N_a r_e \lambda^2 \sum_{i=1}^{N} c_i f_{1i} }{ \pi \sum_{i=1}^{N} c_i M_i } }
</math>
where the ''ci'' the weighting factors (concentration, or stoichiometric numbers in a chemical formula).

==See Also==
* [[Scattering Length Density]]
* [[Refractive index]]

Technical articles

2014-06-05T12:59:26Z

130.199.3.165: /* Scattering techniques */

This page lists the various technical topics that are described on this wiki. Note that many of the topics are currently empty (red links); if you feel qualified, please jump in and contribute!

==Scattering techniques==
* [[SAXS]]/[[SANS]]
** [[USAXS]]/[[USANS]]
** [[CD-SAXS]]/[[RSANS]]
* [[WAXS]]
* [[GISAXS]]
** [[X-ray waveguiding]]
** [[GTSAXS]]
* [[GIWAXS]]
* [[Reflectivity]]
* [[Resonant scattering]]
** [[RSoXS]]

==Kinds of scattering==
* [[Form Factor]]
* [[Structure Factor]]
* [[Diffuse scattering]]
* [[Debye-Waller factor]]
* [[Scattering intensity]]

==Scattering concepts==
* [[Momentum transfer]]
* [[Fourier transform]]
* [[Lattices|Lattice]]
* [[Unit cell]]
* [[Reciprocal-space]]
* [[Ewald sphere]]

==Important quantities==
* [[Atomic scattering factor]]
* [[Scattering Length Density]] (SLD)
* [[Critical angle]]
* [[Refractive index]]
* [[Absorption length]]

==Analysis==
* [[Scherrer grain size analysis]]

==Theory==
* [[DWBA]]

Technical articles

2014-06-05T12:59:13Z

130.199.3.165: /* Scattering techniques */

This page lists the various technical topics that are described on this wiki. Note that many of the topics are currently empty (red links); if you feel qualified, please jump in and contribute!

==Scattering techniques==
* [[SAXS]]/[[SANS]]
** [[USAXS]]/[[USANS]]
** [[CD-SAXS]] ([[RSANS]])
* [[WAXS]]
* [[GISAXS]]
** [[X-ray waveguiding]]
** [[GTSAXS]]
* [[GIWAXS]]
* [[Reflectivity]]
* [[Resonant scattering]]
** [[RSoXS]]

==Kinds of scattering==
* [[Form Factor]]
* [[Structure Factor]]
* [[Diffuse scattering]]
* [[Debye-Waller factor]]
* [[Scattering intensity]]

==Scattering concepts==
* [[Momentum transfer]]
* [[Fourier transform]]
* [[Lattices|Lattice]]
* [[Unit cell]]
* [[Reciprocal-space]]
* [[Ewald sphere]]

==Important quantities==
* [[Atomic scattering factor]]
* [[Scattering Length Density]] (SLD)
* [[Critical angle]]
* [[Refractive index]]
* [[Absorption length]]

==Analysis==
* [[Scherrer grain size analysis]]

==Theory==
* [[DWBA]]

Scattering

2014-06-05T12:57:55Z

130.199.3.165: Created page with "'''Scattering''' broadly refers to experimental techniques that use the interaction between radiation and matter to elucidate structure. In x-ray scattering, a collimated x-ra..."

X9

2014-06-05T12:54:37Z

130.199.3.165:

'''X9''' is an [[x-ray]] [[scattering]] [[synchrotron]] [[beamline]] at the National Synchrotron Light Source ([[NSLS]]), Brookhaven National Lab (BNL). It is a joint beamline between the NSLS and the [http://www.bnl.gov/cfn/ Center for Functional Nanomaterials] (which is a partner user). The instrument is optimized for doing Small-Angle X-ray Scattering ([[SAXS]]) and Grazing-Incidence Small-Angle X-ray Scattering ([[GISAXS]]), as well as wide-angle Grazing-Incidence X-ray Diffraction (GID/GIXD/[[GIWAXS]]).

[[Image:X9_NSLS_01.jpg|400px]][[Image:X9_NSLS_02.jpg|400px]]

==Capabilities==
[[Image:X9-scale.png|center|thumb|600px|X9 hutch layout]]
X9 can perform a variety of x-ray scattering experiments:
* [[SAXS]] and [[WAXS]] on powders or solutions in capillaries. Holder can heat from RT to 80°C.
* [[SAXS/WAXS]] (simultaneous) on proteins or other macromolecules in solution, using a full-vacuum path and a flow-through cell (for robust background subtraction).
* [[GISAXS]] and [[GIWAXS]] on thin films. Sample holder can accommodate multiple samples (for automated measurements), and can heat from RT to 220°C.

==Performance==
===Energy range===
Can perform experiments from 6 keV to 20 keV.

===q-range===
The instrument can capture data on both a SAXS and WAXS detector (either simultaneously or sequentially). The '''q'''-range depends on x-ray energy and the sample-detector distance. For SAXS, one can typically obtain (e.g. for 13.5 keV):
* '''5.4 m''': 0.002 Å−1 to 0.1 Å−1 (314 nm to 6.3 nm)
* '''4.1 m''': 0.005 Å−1 to 0.2 Å−1 (125 nm to 3.5 nm)
* '''3.0 m''': 0.004 Å−1 to 0.2 Å−1 (157 nm to 3.5 nm)
* '''2.0 m''': 0.010 Å−1 to 0.4 Å−1 (63 nm to 1.6 nm)
* '''1.5 m''': 0.011 Å−1 to 0.45 Å−1 (63 nm to 1.4 nm)

For WAXS, standard configurations yields approximately (for 13.5 keV):
* '''0.235 m''' (sample inside chamber): 0.13 Å−1 to 4.1 Å−1 (4.8 nm to 0.15 nm)
* '''~0.4 m''' (sample upstream of chamber): 0.15 Å−1 to 2.1 Å−1 (4.2 nm to 0.3 nm)

===Resolution===
* SAXS: Pixel-limited resolution at 5 m (sample-detector) is ~0.0017°, or 0.0002 Å−1 (at ~13.5 keV).
* WAXS: Pixel-limited resolution is ~0.04°, or 0.0046 Å−1 (at ~13.5 keV). Actual resolution depends on experimental setup and sample size.

===Flux===
* At 10 keV, flux capture by mirrors is ~2×1012 ph/s/0.01%bw
* At 10 keV, flux at sample is ~5×1011 ph/s/0.01%bw
* At 10 keV, microfocused (10 µm), flux at sample is ~2×1011 ph/s/0.01%bw

===Beam Size===
* TSAXS: Typical beam size is ~150 µm horizontal and ~100 µm vertical.
* GISAXS: Typical beam size is ~120 µm horizontal and ~50 µm vertical.
* Microbeam: Beam can be focused to ~15 µm (horizontal and vertical).

==Detectors==
====Dectris Pilatus 1M (SAXS)====
* Hybrid pixel detector.
* [https://www.dectris.com/pilatus3_specifications.html#main_head_navigation Specs]
* Format: 981×1043 = 1,023,183 pixels.
* Pixel size: 172×172 µm2.
* Area: 168.7×179.4 mm2.

====Mar CCD (SAXS)====
* Fiber-coupled CCD detector.
* [http://www.mar-usa.com/support/downloads/sx_series.pdf Specs]
* Outputs 16-bit Grayscale TIFF files with MSB endianess.
* Pixel size (using 1024×1024 binning) is 161 μm (software says 158 um).
* Active area is 165 mm diameter.

====Dectris Pilatus 300k (SAXS)====
* Hybrid pixel detector.
* [http://www.dectris.com/sites/pilatus300k.html Specs]
* Format: 487×619 = 301,453 pixels.
* Pixel size: 172×172 µm2.
* Area: 83.8×106.5 mm2.

====Photonic Science (WAXS)====
* Fiber-coupled CCD detector.
* Outputs 16-bit Grayscale TIFF files with MSB endianess.
* Pixel size (1042×1042): 101.7 μm.
* Detector image is 106 mm in diameter.

==Access==
X9 is available through [http://www.bnl.gov/ps/nsls/users/access/beamtime-new_users.asp NSLS] or [http://www.bnl.gov/cfn/user/ CFN] user programs. However, with [[NSLS]] shutting down permanently in September 2014, new proposals are no longer being accepted.

==Safety==
Users must complete [http://www.bnl.gov/ps/nsls/users/access/training.asp NSLS safety training], as well as receive beamline-specific training:
* [http://beamlines.ps.bnl.gov/forms/BLOSA/X9.pdf X9 BLOSA form]

==See Also==
* [http://www.bnl.gov/ps/x9/ X9 NSLS Official Site]