1 | r""" |
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2 | Definition |
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3 | ---------- |
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4 | |
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5 | This model fits the Guinier function |
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6 | |
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7 | .. math:: I(q) = scale \exp{\left[ \frac{-Q^2R_g^2}{3} \right]} |
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8 | |
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9 | to the data directly without any need for linearisation |
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10 | (*cf*. the usual plot of $\ln I(q)$ vs $q^2$\ ). Note that you may have to |
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11 | restrict the data range to include small q only, where the Guinier approximation |
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12 | actually applies. See also the guinier_porod model. |
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13 | |
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14 | For 2D data the scattering intensity is calculated in the same way as 1D, |
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15 | where the $q$ vector is defined as |
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16 | |
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17 | .. math:: q=\sqrt{q_x^2 + q_y^2} |
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18 | |
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19 | References |
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20 | ---------- |
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21 | |
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22 | A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*, |
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23 | John Wiley & Sons, New York (1955) |
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24 | """ |
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25 | |
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26 | from numpy import inf |
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27 | |
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28 | name = "guinier" |
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29 | title = "" |
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30 | description = """ |
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31 | I(q) = scale.exp ( - rg^2 q^2 / 3.0 ) |
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32 | |
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33 | List of default parameters: |
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34 | scale = scale |
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35 | rg = Radius of gyration |
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36 | """ |
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37 | category = "shape-independent" |
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38 | |
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39 | # ["name", "units", default, [lower, upper], "type","description"], |
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40 | parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of Gyration"]] |
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41 | |
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42 | Iq = """ |
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43 | double exponent = rg*rg*q*q/3.0; |
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44 | double value = exp(-exponent); |
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45 | return value; |
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46 | """ |
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47 | |
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48 | Iqxy = """ |
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49 | return Iq(sqrt(qx*qx + qy*qy), rg); |
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50 | """ |
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51 | |
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52 | # parameters for demo |
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53 | demo = dict(scale=1.0, rg=60.0) |
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54 | |
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55 | # parameters for unit tests |
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56 | tests = [[{'rg' : 31.5}, 0.005, 0.992756]] |
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