Changeset c3ccaec in sasmodels for sasmodels/models/unified_power_Rg.py

Timestamp:

Feb 7, 2017 12:10:50 PM (7 years ago)

Author:

GitHub <noreply@…>

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

a90aa1c

Parents:

aa107ef (diff), fe8ff99 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

git-author:

Paul Kienzle <pkienzle@…> (02/07/17 12:10:50)

git-committer:

GitHub <noreply@…> (02/07/17 12:10:50)

Message:

Merge branch 'master' into ticket-815

File:

• sasmodels/models/unified_power_Rg.py (modified) (4 diffs)

sasmodels/models/unified_power_Rg.py

@@ -3 +3 @@
 ----------
 
-The Beaucage model employs the empirical multiple level unified
-Exponential/Power-law fit method developed by G. Beaucage. Four functions
-are included so that 1, 2, 3, or 4 levels can be used. In addition a 0 level
-has been added which simply calculates
+This model employs the empirical multiple level unified Exponential/Power-law 
+fit method developed by Beaucage. Four functions are included so that 1, 2, 3, 
+or 4 levels can be used. In addition a 0 level has been added which simply 
+calculates
 
 .. math::
@@ -15 +15 @@
 many different types of particles, including fractal clusters, random coils
 (Debye equation), ellipsoidal particles, etc.
+
+The model works best for mass fractal systems characterized by Porod exponents 
+between 5/3 and 3. It should not be used for surface fractal systems. Hammouda 
+(2010) has pointed out a deficiency in the way this model handles the 
+transitioning between the Guinier and Porod regimes and which can create 
+artefacts that appear as kinks in the fitted model function.
+
+Also see the Guinier_Porod model.
 
 The empirical fit function is:
@@ -30 +38 @@
 .. math::
 
-    q_i^* = \frac{q}{\operatorname{erf}^3(q R_{gi}/\sqrt{6}}
+    q_i^* = q \left[\operatorname{erf}
+            \left(\frac{q R_{gi}}{\sqrt{6}}\right)
+        \right]^{-3}
 
 
@@ -56 +66 @@
 
 G Beaucage, *J. Appl. Cryst.*, 29 (1996) 134-146
+
+B Hammouda, *Analysis of the Beaucage model, J. Appl. Cryst.*, (2010), 43, 1474-1478
 
 """