Changeset 7c391dd in sasmodels for sasmodels/models/lamellar.py

Timestamp:

Mar 18, 2016 8:18:56 AM (8 years ago)

Author:

richardh

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:

d5ba841

Parents:

9538fae

Message:

checked lamellar, reordered params, improved docs

File:

• sasmodels/models/lamellar.py (modified) (5 diffs)

sasmodels/models/lamellar.py

@@ -5 +5 @@
 ----------
 
-The scattering intensity $I(q)$ is
+The scattering intensity $I(q)$ for dilute, randomly oriented, "infinitely large" sheets or lamellae is
 
 .. math::
 
-    I(q) = \frac{2\pi P(q)}{\delta q^2}
+    I(q) = scale*\frac{2\pi P(q)}{q^2\delta }
 
 
@@ -16 +16 @@
 .. math::
 
-    P(q) = \frac{2\Delta\rho^2}{q^2}(1-cos(q\delta))
+   P(q) = \frac{2\Delta\rho^2}{q^2}(1-cos(q\delta)) = \frac{4\Delta\rho^2}{q^2}sin^2(\frac{q\delta}{2})
 
+where $\delta$ is the total layer thickness and $\Delta\rho$ is the scattering length density difference.
 
-where $\delta$ is the bilayer thickness.
+This is the limiting form for a spherical shell of infinitely large radius. Note that the division by $\delta$
+means that $scale$ in sasview is the volume fraction of sheet, $\phi = S\delta$ where $S$ is the area of 
+sheet per unit volume. $S$ is half the Porod surface area per unit volume of a thicker layer (as that would 
+include both faces of the sheet).
 
 The 2D scattering intensity is calculated in the same way as 1D, where
@@ -56 +60 @@
 
 #             ["name", "units", default, [lower, upper], "type","description"],
-parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "",
-               "Layer scattering length density" ],
-              ["solvent_sld", "1e-6/Ang^2", 6, [-inf, inf], "",
-               "Solvent scattering length density" ],
-              ["thickness", "Ang", 50, [0, inf], "volume","Bilayer thickness" ],
+parameters = [ ["thickness", "Ang", 50, [0, inf], "volume","total layer thickness" ],
+               ["sld", "1e-6/Ang^2", 1, [-inf, inf], "","Layer scattering length density" ],
+               ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "","Solvent scattering length density" ],
              ]
 
-
 # No volume normalization despite having a volume parameter
-# This should perhaps be volume normalized?
+# This should perhaps be volume normalized? - it is!
 form_volume = """
     return 1.0;
@@ -71 +72 @@
 
 Iq = """
-    const double sub = sld - solvent_sld;
+    const double sub = sld - sld_solvent;
     const double qsq = q*q;
     // Original expression
@@ -89 +90 @@
 
 demo = dict(scale=1, background=0,
-            sld=6, solvent_sld=1,
+            sld=6, sld_solvent=1,
             thickness=40,
             thickness_pd=0.2, thickness_pd_n=40)
 oldname = 'LamellarModel'
-oldpars = dict(sld='sld_bi', solvent_sld='sld_sol', thickness='bi_thick')
+oldpars = dict(sld='sld_bi', sld_solvent='sld_sol', thickness='bi_thick')
 tests = [
-        [ {'scale': 1.0, 'background' : 0.0, 'thickness' : 50.0, 'sld' : 1.0,'solvent_sld' : 6.3, 'thickness_pd' : 0.0, 
+        [ {'scale': 1.0, 'background' : 0.0, 'thickness' : 50.0, 'sld' : 1.0,'sld_solvent' : 6.3, 'thickness_pd' : 0.0, 
            }, [0.001], [882289.54309]]
         ]