[80768fc] | 1 | r""" |
---|
| 2 | |
---|
| 3 | Scattering model class for the DAB (Debye Anderson Brumberger) Model |
---|
| 4 | |
---|
| 5 | Definition |
---|
| 6 | ---------- |
---|
| 7 | |
---|
[f224873] | 8 | Calculates the scattering from a randomly distributed, two-phase system based on |
---|
| 9 | the Debye-Anderson-Brumberger (DAB) model for such systems. The two-phase system |
---|
| 10 | is characterized by a single length scale, the correlation length, which is a |
---|
| 11 | measure of the average spacing between regions of phase 1 and phase 2. **The |
---|
| 12 | model also assumes smooth interfaces between the phases** and hence exhibits |
---|
| 13 | Porod behavior (I ~ *q*\ :sup:`-4`) at large *q* (*QL* >> 1). |
---|
[80768fc] | 14 | |
---|
| 15 | The DAB model is ostensibly a development of the earlier Debye-Bueche model. |
---|
| 16 | |
---|
[f224873] | 17 | *Definition* |
---|
[80768fc] | 18 | |
---|
[f224873] | 19 | .. math:: I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q \cdot L)^2)^2} + \text{background} |
---|
[80768fc] | 20 | |
---|
| 21 | where scale is |
---|
| 22 | |
---|
| 23 | .. math:: \text{scale} = 8 \pi \phi (1-\phi)(\Delta \rho)^2 |
---|
| 24 | |
---|
[f224873] | 25 | and the parameter *L* is the correlation length. |
---|
| 26 | |
---|
| 27 | For 2D data: The 2D scattering intensity is calculated in the same way as 1D, |
---|
| 28 | where the *q* vector is defined as |
---|
| 29 | |
---|
| 30 | .. math:: q = \sqrt{q_x^2 + q_y^2} |
---|
| 31 | |
---|
| 32 | ============== ======== ============= |
---|
| 33 | Parameter name Units Default value |
---|
| 34 | ============== ======== ============= |
---|
| 35 | scale None 1.0 |
---|
| 36 | corr length L |Ang| 50.0 |
---|
| 37 | background |cm^-1| 0.0 |
---|
| 38 | ============== ======== ============= |
---|
| 39 | |
---|
| 40 | |
---|
| 41 | .. figure:: img/dab_1d.jpg |
---|
| 42 | |
---|
| 43 | 1D plot using the default values (w/200 data point). |
---|
| 44 | |
---|
| 45 | |
---|
[80768fc] | 46 | Reference |
---|
| 47 | --------- |
---|
| 48 | |
---|
[f224873] | 49 | P Debye, H R Anderson, H Brumberger, *Scattering by an Inhomogeneous Solid. II. |
---|
| 50 | The Correlation Function and its Application*, *J. Appl. Phys.*, 28(6) (1957) 679 |
---|
[80768fc] | 51 | |
---|
[f224873] | 52 | P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, |
---|
| 53 | 20 (1949) 518 |
---|
[80768fc] | 54 | |
---|
| 55 | *2013/09/09 - Description reviewed by King, S and Parker, P.* |
---|
| 56 | |
---|
| 57 | """ |
---|
| 58 | |
---|
| 59 | from numpy import inf |
---|
| 60 | |
---|
| 61 | name = "dab" |
---|
| 62 | title = "DAB (Debye Anderson Brumberger) Model" |
---|
| 63 | description = """\ |
---|
| 64 | |
---|
[f224873] | 65 | F(q)= scale * L^3/(1 + (q*L)^2)^2 |
---|
[80768fc] | 66 | |
---|
| 67 | L: the correlation length |
---|
| 68 | |
---|
| 69 | """ |
---|
[a5d0d00] | 70 | category = "shape-independent" |
---|
[80768fc] | 71 | |
---|
[3e428ec] | 72 | # ["name", "units", default, [lower, upper], "type", "description"], |
---|
| 73 | parameters = [["length", "Ang", 50.0, [0, inf], "", "correlation length"], |
---|
| 74 | ] |
---|
[80768fc] | 75 | |
---|
| 76 | Iq = """ |
---|
| 77 | double numerator = pow(length, 3); |
---|
| 78 | double denominator = pow(1 + pow(q*length,2), 2); |
---|
| 79 | |
---|
| 80 | return numerator / denominator ; |
---|
| 81 | """ |
---|
| 82 | |
---|
| 83 | Iqxy = """ |
---|
| 84 | // never called since no orientation or magnetic parameters. |
---|
| 85 | //return -1.0; |
---|
| 86 | return Iq(sqrt(qx*qx + qy*qy), length); |
---|
| 87 | """ |
---|
| 88 | |
---|
| 89 | # ER defaults to 1.0 |
---|
| 90 | |
---|
| 91 | # VR defaults to 1.0 |
---|
| 92 | |
---|
[3e428ec] | 93 | demo = dict(scale=1, background=0, length=50) |
---|
[80768fc] | 94 | oldname = "DABModel" |
---|
| 95 | oldpars = dict(length='length') |
---|