[68532f3] | 1 | .. _sphere: |
---|
| 2 | |
---|
| 3 | Sphere |
---|
| 4 | ======================================================= |
---|
| 5 | |
---|
| 6 | Spheres with uniform scattering length density |
---|
| 7 | |
---|
| 8 | =========== ================================= ============ ============= |
---|
| 9 | Parameter Description Units Default value |
---|
| 10 | =========== ================================= ============ ============= |
---|
| 11 | scale Source intensity None 1 |
---|
| 12 | background Source background |cm^-1| 0 |
---|
| 13 | sld Layer scattering length density |1e-6Ang^-2| 1 |
---|
| 14 | solvent_sld Solvent scattering length density |1e-6Ang^-2| 6 |
---|
| 15 | radius Sphere radius |Ang| 50 |
---|
| 16 | =========== ================================= ============ ============= |
---|
| 17 | |
---|
| 18 | The returned value is scaled to units of |cm^-1|. |
---|
| 19 | |
---|
| 20 | |
---|
[d1fe925] | 21 | For information about polarised and magnetic scattering, click here_. |
---|
| 22 | |
---|
| 23 | .. _here: polar_mag_help.html |
---|
| 24 | |
---|
| 25 | Definition |
---|
| 26 | ---------- |
---|
| 27 | |
---|
| 28 | The 1D scattering intensity is calculated in the following way (Guinier, 1955) |
---|
| 29 | |
---|
| 30 | .. math:: |
---|
| 31 | |
---|
| 32 | I(Q) = \frac{\text{scale}}{V} \cdot \left[ \ |
---|
| 33 | 3V(\Delta\rho) \cdot \frac{\sin(QR) - QR\cos(QR))}{(QR)^3} \ |
---|
| 34 | \right]^2 + \text{background} |
---|
| 35 | |
---|
| 36 | where *scale* is a volume fraction, $V$ is the volume of the scatterer, |
---|
| 37 | $R$ is the radius of the sphere, *background* is the background level and |
---|
| 38 | *sld* and *solvent_sld* are the scattering length densities (SLDs) of the |
---|
| 39 | scatterer and the solvent respectively. |
---|
| 40 | |
---|
| 41 | Note that if your data is in absolute scale, the *scale* should represent |
---|
| 42 | the volume fraction (which is unitless) if you have a good fit. If not, |
---|
| 43 | it should represent the volume fraction times a factor (by which your data |
---|
| 44 | might need to be rescaled). |
---|
| 45 | |
---|
| 46 | The 2D scattering intensity is the same as above, regardless of the |
---|
| 47 | orientation of $\vec q$. |
---|
| 48 | |
---|
| 49 | Our model uses the form factor calculations as defined in the IGOR |
---|
| 50 | package provided by the NIST Center for Neutron Research (Kline, 2006). |
---|
| 51 | |
---|
| 52 | Validation |
---|
| 53 | ---------- |
---|
| 54 | |
---|
| 55 | Validation of our code was done by comparing the output of the 1D model |
---|
| 56 | to the output of the software provided by the NIST (Kline, 2006). |
---|
| 57 | Figure :num:`figure #sphere-comparison` shows a comparison of the output |
---|
| 58 | of our model and the output of the NIST software. |
---|
| 59 | |
---|
| 60 | .. _sphere-comparison: |
---|
| 61 | |
---|
| 62 | .. figure:: img/sphere_comparison.jpg |
---|
| 63 | |
---|
| 64 | Comparison of the DANSE scattering intensity for a sphere with the |
---|
| 65 | output of the NIST SANS analysis software. The parameters were set to: |
---|
| 66 | *scale* = 1.0, *radius* = 60 |Ang|, *contrast* = 1e-6 |Ang^-2|, and |
---|
| 67 | *background* = 0.01 |cm^-1|. |
---|
| 68 | |
---|
| 69 | |
---|
| 70 | Reference |
---|
| 71 | --------- |
---|
| 72 | |
---|
| 73 | A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, |
---|
| 74 | John Wiley and Sons, New York, (1955) |
---|
| 75 | |
---|
| 76 | *2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.* |
---|
[68532f3] | 77 | |
---|