Changeset f224873 in sasmodels


Ignore:
Timestamp:
Jul 25, 2015 7:29:44 PM (7 years ago)
Author:
butler
Branches:
master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
346bc88
Parents:
f3f46cd
Message:

updated documentation - see ticket #400

File:
1 edited

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  • sasmodels/models/dab.py

    r3e428ec rf224873  
    66---------- 
    77 
    8 Calculates the scattering from a randomly distributed, two-phase system based on the Debye-Anderson-Brumberger (DAB) 
    9 model for such systems. The two-phase 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). 
     8Calculates the scattering from a randomly distributed, two-phase system based on 
     9the Debye-Anderson-Brumberger (DAB) model for such systems. The two-phase system 
     10is characterized by a single length scale, the correlation length, which is a 
     11measure of the average spacing between regions of phase 1 and phase 2. **The 
     12model also assumes smooth interfaces between the phases** and hence exhibits 
     13Porod behavior (I ~ *q*\ :sup:`-4`) at large *q* (*QL* >> 1). 
    1214 
    1315The DAB model is ostensibly a development of the earlier Debye-Bueche model. 
    1416 
    15 .. figure:: img/dab_1d.jpg 
     17*Definition* 
    1618 
    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} 
    1820 
    1921where scale is 
     
    2123.. math:: \text{scale} = 8 \pi \phi (1-\phi)(\Delta \rho)^2 
    2224 
     25and the parameter *L* is the correlation length. 
     26 
     27For 2D data: The 2D scattering intensity is calculated in the same way as 1D, 
     28where the *q* vector is defined as 
     29 
     30.. math:: q = \sqrt{q_x^2 + q_y^2} 
     31 
     32==============  ========  ============= 
     33Parameter name  Units     Default value 
     34==============  ========  ============= 
     35scale           None      1.0 
     36corr length L   |Ang|     50.0 
     37background      |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 
    2346Reference 
    2447--------- 
    2548 
    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) 679 
     49P Debye, H R Anderson, H Brumberger, *Scattering by an Inhomogeneous Solid. II. 
     50The Correlation Function and its Application*, *J. Appl. Phys.*, 28(6) (1957) 679 
    2851 
    29 P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 20 (1949) 518 
     52P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 
     5320 (1949) 518 
    3054 
    3155*2013/09/09 - Description reviewed by King, S and Parker, P.* 
     
    3963description = """\ 
    4064 
    41 F(q)= L^3/(1 + (q*L)^2)^2 
     65F(q)= scale * L^3/(1 + (q*L)^2)^2 
    4266 
    4367L: the correlation length 
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