[80768fc] | 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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[a5d0d00] | 46 | category = "shape-independent" |
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[80768fc] | 47 | |
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[3e428ec] | 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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[80768fc] | 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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[3e428ec] | 69 | demo = dict(scale=1, background=0, length=50) |
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[80768fc] | 70 | oldname = "DABModel" |
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| 71 | oldpars = dict(length='length') |
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