| 1 | .. _dab: |
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| 2 | |
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| 3 | Dab |
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| 4 | ======================================================= |
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| 5 | |
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| 6 | DAB (Debye Anderson Brumberger) Model |
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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 | length correlation length |Ang| 50 |
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| 14 | ========== ================== ======= ============= |
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| 15 | |
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| 16 | The returned value is scaled to units of |cm^-1|. |
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| 17 | |
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| 18 | |
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| 19 | |
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| 20 | Scattering model class for the DAB (Debye Anderson Brumberger) Model |
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| 21 | |
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| 22 | Definition |
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| 23 | ---------- |
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| 24 | |
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| 25 | Calculates the scattering from a randomly distributed, two-phase system based on |
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| 26 | the Debye-Anderson-Brumberger (DAB) model for such systems. The two-phase system |
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| 27 | is characterized by a single length scale, the correlation length, which is a |
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| 28 | measure of the average spacing between regions of phase 1 and phase 2. **The |
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| 29 | model also assumes smooth interfaces between the phases** and hence exhibits |
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| 30 | Porod behavior (I ~ *q*\ :sup:`-4`) at large *q* (*QL* >> 1). |
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| 31 | |
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| 32 | The DAB model is ostensibly a development of the earlier Debye-Bueche model. |
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| 33 | |
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| 34 | *Definition* |
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| 35 | |
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| 36 | .. math:: I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q \cdot L)^2)^2} + \text{background} |
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| 37 | |
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| 38 | where scale is |
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| 39 | |
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| 40 | .. math:: \text{scale} = 8 \pi \phi (1-\phi)(\Delta \rho)^2 |
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| 41 | |
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| 42 | and the parameter *L* is the correlation length. |
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| 43 | |
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| 44 | For 2D data: The 2D scattering intensity is calculated in the same way as 1D, |
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| 45 | where the *q* vector is defined as |
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| 46 | |
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| 47 | .. math:: q = \sqrt{q_x^2 + q_y^2} |
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| 48 | |
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| 49 | ============== ======== ============= |
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| 50 | Parameter name Units Default value |
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| 51 | ============== ======== ============= |
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| 52 | scale None 1.0 |
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| 53 | corr length L |Ang| 50.0 |
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| 54 | background |cm^-1| 0.0 |
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| 55 | ============== ======== ============= |
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| 56 | |
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| 57 | |
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| 58 | .. figure:: img/dab_1d.jpg |
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| 59 | |
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| 60 | 1D plot using the default values (w/200 data point). |
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| 61 | |
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| 62 | |
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| 63 | Reference |
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| 64 | --------- |
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| 65 | |
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| 66 | P Debye, H R Anderson, H Brumberger, *Scattering by an Inhomogeneous Solid. II. |
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| 67 | The Correlation Function and its Application*, *J. Appl. Phys.*, 28(6) (1957) 679 |
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| 68 | |
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| 69 | P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, |
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| 70 | 20 (1949) 518 |
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| 71 | |
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| 72 | *2013/09/09 - Description reviewed by King, S and Parker, P.* |
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| 73 | |
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| 74 | |
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