1 | r""" |
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2 | |
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3 | Scattering model class for the DAB (Debye Anderson Brumberger) Model |
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4 | |
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5 | Definition |
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6 | ---------- |
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7 | |
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8 | Calculates the scattering from a randomly distributed, two-phase system based on the Debye-Anderson-Brumberger (DAB) |
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9 | model for such systems. The two-phase system is characterized by a single length scale, the correlation length, which |
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10 | is a measure of the average spacing between regions of phase 1 and phase 2. **The model also assumes smooth interfaces** |
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11 | **between the phases** and hence exhibits Porod behavior (I ~ *q*\ :sup:`-4`) at large *q* (*QL* >> 1). |
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12 | |
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13 | The DAB model is ostensibly a development of the earlier Debye-Bueche model. |
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14 | |
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15 | .. figure:: img/dab_1d.jpg |
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16 | |
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17 | .. math:: I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q L)^2)^2} + \text{background} |
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18 | |
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19 | where scale is |
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20 | |
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21 | .. math:: \text{scale} = 8 \pi \phi (1-\phi)(\Delta \rho)^2 |
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22 | |
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23 | Reference |
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24 | --------- |
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25 | |
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26 | P Debye, H R Anderson, H Brumberger, *Scattering by an Inhomogeneous Solid. II. The Correlation Function* |
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27 | *and its Application*, *J. Appl. Phys.*, 28(6) (1957) 679 |
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28 | |
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29 | P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 20 (1949) 518 |
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30 | |
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31 | *2013/09/09 - Description reviewed by King, S and Parker, P.* |
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32 | |
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33 | """ |
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34 | |
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35 | from numpy import inf |
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36 | |
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37 | name = "dab" |
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38 | title = "DAB (Debye Anderson Brumberger) Model" |
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39 | description = """\ |
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40 | |
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41 | F(q)= L^3/(1 + (q*L)^2)^2 |
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42 | |
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43 | L: the correlation length |
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44 | |
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45 | """ |
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46 | category = "shape-independent" |
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47 | |
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48 | # ["name", "units", default, [lower, upper], "type", "description"], |
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49 | parameters = [["length", "Ang", 50.0, [0, inf], "", "correlation length"], |
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50 | ] |
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51 | |
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52 | Iq = """ |
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53 | double numerator = pow(length, 3); |
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54 | double denominator = pow(1 + pow(q*length,2), 2); |
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55 | |
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56 | return numerator / denominator ; |
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57 | """ |
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58 | |
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59 | Iqxy = """ |
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60 | // never called since no orientation or magnetic parameters. |
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61 | //return -1.0; |
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62 | return Iq(sqrt(qx*qx + qy*qy), length); |
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63 | """ |
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64 | |
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65 | # ER defaults to 1.0 |
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66 | |
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67 | # VR defaults to 1.0 |
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68 | |
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69 | demo = dict(scale=1, background=0, length=50) |
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70 | oldname = "DABModel" |
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71 | oldpars = dict(length='length') |
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