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