Changeset f224873 in sasmodels
 Timestamp:
 Jul 25, 2015 7:29:44 PM (7 years ago)
 Branches:
 master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket1257vesicleproduct, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
 Children:
 346bc88
 Parents:
 f3f46cd
 File:

 1 edited
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sasmodels/models/dab.py
r3e428ec rf224873 6 6  7 7 8 Calculates the scattering from a randomly distributed, twophase system based on the DebyeAndersonBrumberger (DAB) 9 model for such systems. The twophase system is characterized by a single length scale, the correlation length, which 10 is a measure of the average spacing between regions of phase 1 and phase 2. **The model also assumes smooth interfaces** 11 **between the phases** and hence exhibits Porod behavior (I ~ *q*\ :sup:`4`) at large *q* (*QL* >> 1). 8 Calculates the scattering from a randomly distributed, twophase system based on 9 the DebyeAndersonBrumberger (DAB) model for such systems. The twophase 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). 12 14 13 15 The DAB model is ostensibly a development of the earlier DebyeBueche model. 14 16 15 .. figure:: img/dab_1d.jpg 17 *Definition* 16 18 17 .. math:: I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q L)^2)^2} + \text{background}19 .. math:: I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q \cdot L)^2)^2} + \text{background} 18 20 19 21 where scale is … … 21 23 .. math:: \text{scale} = 8 \pi \phi (1\phi)(\Delta \rho)^2 22 24 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 23 46 Reference 24 47  25 48 26 P Debye, H R Anderson, H Brumberger, *Scattering by an Inhomogeneous Solid. II. The Correlation Function*27 *and its Application*, *J. Appl. Phys.*, 28(6) (1957) 67949 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 28 51 29 P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 20 (1949) 518 52 P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 53 20 (1949) 518 30 54 31 55 *2013/09/09  Description reviewed by King, S and Parker, P.* … … 39 63 description = """\ 40 64 41 F(q)= L^3/(1 + (q*L)^2)^265 F(q)= scale * L^3/(1 + (q*L)^2)^2 42 66 43 67 L: the correlation length
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